diff --git a/packages/babel-plugin-proposal-class-static-block/package.json b/packages/babel-plugin-proposal-class-static-block/package.json
index 08d2357fcc14..4ba6e6b1a6d6 100644
--- a/packages/babel-plugin-proposal-class-static-block/package.json
+++ b/packages/babel-plugin-proposal-class-static-block/package.json
@@ -23,6 +23,6 @@
     "@babel/plugin-syntax-class-static-block": "workspace:^7.11.0"
   },
   "peerDependencies": {
-    "@babel/core": "^7.0.0-0"
+    "@babel/core": "^7.12.0"
   }
 }
diff --git a/packages/babel-plugin-proposal-class-static-block/src/index.js b/packages/babel-plugin-proposal-class-static-block/src/index.js
index 82589b3a5caa..2ff1361c289a 100644
--- a/packages/babel-plugin-proposal-class-static-block/src/index.js
+++ b/packages/babel-plugin-proposal-class-static-block/src/index.js
@@ -2,50 +2,28 @@ import { declare } from "@babel/helper-plugin-utils";
 import syntaxClassStaticBlock from "@babel/plugin-syntax-class-static-block";
 
 export default declare(({ types: t, template, assertVersion }) => {
-  assertVersion(7);
+  // todo remove this check after Babel 7.12.0 is published
+  if (process.env.NODE_ENV !== "test") {
+    assertVersion("^7.12.0");
+  }
 
   return {
     name: "proposal-class-static-block",
     inherits: syntaxClassStaticBlock,
     visitor: {
       StaticBlock(path) {
-        const staticBlockRef = path.scope.generateUidIdentifier("init");
-        const classPath = path.parentPath.parentPath;
-        path.replaceWith(
-          t.classMethod(
-            "method",
-            staticBlockRef,
+        const staticBlockRef = path.scope.generateUidIdentifier("");
+        const classBody = path.parentPath;
+        classBody.pushContainer(
+          "body",
+          t.classPrivateProperty(
+            t.privateName(staticBlockRef),
+            template.expression.ast`(() => { ${path.node.body} })()`,
             [],
-            t.BlockStatement(
-              // Add completion record. A static block can not contain directly
-              // `return`, `break`, `continue`. So `return this` must be executed.
-              path.node.body.concat([
-                template.ast`delete this.${t.cloneNode(staticBlockRef)};`,
-                template.ast`return this;`,
-              ]),
-            ),
-            /* computed */ false,
             /* static */ true,
           ),
         );
-        const classId = classPath.node.id;
-        if (!classId) {
-          // If `classId` is not defined, we don't have to preserve the class binding
-          // `class { }` transformed as `(class { })._init()`
-          classPath.replaceWith(
-            template.ast`(${classPath.node}).${t.cloneNode(staticBlockRef)}()`,
-          );
-        } else {
-          // If `classId` is defined, preserve the class binding.
-          // `class Foo { }` transformed as `(Foo = (class Foo { })._init())`
-          classPath.node.type = "ClassExpression";
-          classPath.replaceWith(
-            template.ast`${t.cloneNode(classId)} = (${
-              classPath.node
-            }).${t.cloneNode(staticBlockRef)}()`,
-          );
-          classPath.insertBefore(template.ast`let ${t.cloneNode(classId)};`);
-        }
+        path.remove();
       },
     },
   };
diff --git a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-binding/exec.js b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-binding/exec.js
new file mode 100644
index 000000000000..aea35fe5c6ec
--- /dev/null
+++ b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-binding/exec.js
@@ -0,0 +1,7 @@
+class Foo {
+  static {
+    this.foo = Foo.bar;
+  }
+  static bar = 42;
+}
+expect(Foo.foo).toBe(42);
diff --git a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-declaration/exec.js b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-declaration/exec.js
index 719d9f22eb77..a748d4ad1f2e 100644
--- a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-declaration/exec.js
+++ b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-declaration/exec.js
@@ -1,6 +1,7 @@
 class Foo {
   static {
-    this.foo = 42;
+    this.foo = this.bar;
   }
+  static bar = 42;
 }
 expect(Foo.foo).toBe(42);
diff --git a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-declaration/input.js b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-declaration/input.js
index 719d9f22eb77..a748d4ad1f2e 100644
--- a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-declaration/input.js
+++ b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-declaration/input.js
@@ -1,6 +1,7 @@
 class Foo {
   static {
-    this.foo = 42;
+    this.foo = this.bar;
   }
+  static bar = 42;
 }
 expect(Foo.foo).toBe(42);
diff --git a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-declaration/output.js b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-declaration/output.js
index d63d3c46db77..49139ba432a1 100644
--- a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-declaration/output.js
+++ b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-declaration/output.js
@@ -1,10 +1,8 @@
-let Foo;
-Foo = class Foo {
-  static _init() {
-    this.foo = 42;
-    delete this._init;
-    return this;
-  }
+class Foo {
+  static bar = 42;
+  static #_ = (() => {
+    this.foo = this.bar;
+  })();
+}
 
-}._init();
 expect(Foo.foo).toBe(42);
diff --git a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-expression/options.json b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-expression/options.json
deleted file mode 100644
index 7d950d213e02..000000000000
--- a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/class-expression/options.json
+++ /dev/null
@@ -1,3 +0,0 @@
-{
-  "plugins": ["proposal-class-static-block", "syntax-class-properties"]
-}
diff --git a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage-named/exec.js b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage-named/exec.js
deleted file mode 100644
index 9bc06b9a8017..000000000000
--- a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage-named/exec.js
+++ /dev/null
@@ -1,10 +0,0 @@
-class Foo extends class {
-  static {
-    this.bar = 21;
-  }
-} {
-  static {
-    this.foo = 2 * this.bar;
-  }
-}
-expect(Foo.foo).toBe(42);
diff --git a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage-named/input.js b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage-named/input.js
deleted file mode 100644
index 27c55d931eca..000000000000
--- a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage-named/input.js
+++ /dev/null
@@ -1,10 +0,0 @@
-class Foo extends class Bar {
-  static {
-    this.bar = 21;
-  }
-} {
-  static {
-    this.foo = 2 * this.bar;
-  }
-}
-expect(Foo.foo).toBe(42);
diff --git a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage-named/output.js b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage-named/output.js
deleted file mode 100644
index 89f4839a0171..000000000000
--- a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage-named/output.js
+++ /dev/null
@@ -1,18 +0,0 @@
-let Foo;
-let Bar;
-Foo = class Foo extends (Bar = class Bar {
-  static _init2() {
-    this.bar = 21;
-    delete this._init2;
-    return this;
-  }
-
-}._init2()) {
-  static _init() {
-    this.foo = 2 * this.bar;
-    delete this._init;
-    return this;
-  }
-
-}._init();
-expect(Foo.foo).toBe(42);
diff --git a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage/exec.js b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage/exec.js
index 9bc06b9a8017..be708dae2b0d 100644
--- a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage/exec.js
+++ b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage/exec.js
@@ -1,10 +1,14 @@
-class Foo extends class {
+class Foo extends class extends class Base {
+  static {
+    this.qux = 21;
+  }
+} {
   static {
     this.bar = 21;
   }
 } {
   static {
-    this.foo = 2 * this.bar;
+    this.foo = this.bar + this.qux;
   }
 }
 expect(Foo.foo).toBe(42);
diff --git a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage/input.js b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage/input.js
index 9bc06b9a8017..be708dae2b0d 100644
--- a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage/input.js
+++ b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage/input.js
@@ -1,10 +1,14 @@
-class Foo extends class {
+class Foo extends class extends class Base {
+  static {
+    this.qux = 21;
+  }
+} {
   static {
     this.bar = 21;
   }
 } {
   static {
-    this.foo = 2 * this.bar;
+    this.foo = this.bar + this.qux;
   }
 }
 expect(Foo.foo).toBe(42);
diff --git a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage/output.js b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage/output.js
index 24eb243c9155..256b0f546814 100644
--- a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage/output.js
+++ b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/in-class-heritage/output.js
@@ -1,17 +1,15 @@
-let Foo;
-Foo = class Foo extends class {
-  static _init2() {
+class Foo extends class extends class Base {
+  static #_3 = (() => {
+    this.qux = 21;
+  })();
+} {
+  static #_2 = (() => {
     this.bar = 21;
-    delete this._init2;
-    return this;
-  }
+  })();
+} {
+  static #_ = (() => {
+    this.foo = this.bar + this.qux;
+  })();
+}
 
-}._init2() {
-  static _init() {
-    this.foo = 2 * this.bar;
-    delete this._init;
-    return this;
-  }
-
-}._init();
 expect(Foo.foo).toBe(42);
diff --git a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/multiple-static-initializers/exec.js b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/multiple-static-initializers/exec.js
new file mode 100644
index 000000000000..657be074147c
--- /dev/null
+++ b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/multiple-static-initializers/exec.js
@@ -0,0 +1,8 @@
+class Foo {
+  static #bar = 21;
+  static {
+    this.foo = this.#bar + this.qux;
+  }
+  static qux = 21;
+}
+expect(Foo.foo).toBe(42);
diff --git a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/private-elements-access/options.json b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/options.json
similarity index 100%
rename from packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/private-elements-access/options.json
rename to packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/options.json
diff --git a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/super-property/options.json b/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/super-property/options.json
deleted file mode 100644
index 7d950d213e02..000000000000
--- a/packages/babel-plugin-proposal-class-static-block/test/fixtures/class-static-block/super-property/options.json
+++ /dev/null
@@ -1,3 +0,0 @@
-{
-  "plugins": ["proposal-class-static-block", "syntax-class-properties"]
-}
diff --git a/packages/babel-types/src/definitions/experimental.js b/packages/babel-types/src/definitions/experimental.js
index d9e0b9879a8b..e11581704963 100644
--- a/packages/babel-types/src/definitions/experimental.js
+++ b/packages/babel-types/src/definitions/experimental.js
@@ -108,7 +108,7 @@ defineType("PipelinePrimaryTopicReference", {
 
 defineType("ClassPrivateProperty", {
   visitor: ["key", "value", "decorators"],
-  builder: ["key", "value", "decorators"],
+  builder: ["key", "value", "decorators", "static"],
   aliases: ["Property", "Private"],
   fields: {
     key: {
diff --git a/yarn.lock b/yarn.lock
index 034aa2850fbd..32c403f647a8 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -1011,7 +1011,7 @@ __metadata:
     "@babel/helper-plugin-utils": "workspace:^7.10.1"
     "@babel/plugin-syntax-class-static-block": "workspace:^7.11.0"
   peerDependencies:
-    "@babel/core": ^7.0.0-0
+    "@babel/core": ^7.12.0
   languageName: unknown
   linkType: soft