diff --git a/packages/eslint-plugin/src/rules/no-invalid-void-type.ts b/packages/eslint-plugin/src/rules/no-invalid-void-type.ts
index 7cda184e4fdc..9f938ac438f7 100644
--- a/packages/eslint-plugin/src/rules/no-invalid-void-type.ts
+++ b/packages/eslint-plugin/src/rules/no-invalid-void-type.ts
@@ -13,7 +13,8 @@ type MessageIds =
   | 'invalidVoidNotReturnOrGeneric'
   | 'invalidVoidNotReturn'
   | 'invalidVoidNotReturnOrThisParam'
-  | 'invalidVoidNotReturnOrThisParamOrGeneric';
+  | 'invalidVoidNotReturnOrThisParamOrGeneric'
+  | 'invalidVoidUnionConstituent';
 
 export default util.createRule<[Options], MessageIds>({
   name: 'no-invalid-void-type',
@@ -25,14 +26,16 @@ export default util.createRule<[Options], MessageIds>({
     },
     messages: {
       invalidVoidForGeneric:
-        '{{ generic }} may not have void as a type variable.',
+        '{{ generic }} may not have void as a type argument.',
       invalidVoidNotReturnOrGeneric:
-        'void is only valid as a return type or generic type variable.',
+        'void is only valid as a return type or generic type argument.',
       invalidVoidNotReturn: 'void is only valid as a return type.',
       invalidVoidNotReturnOrThisParam:
         'void is only valid as return type or type of `this` parameter.',
       invalidVoidNotReturnOrThisParamOrGeneric:
-        'void is only valid as a return type or generic type variable or the type of a `this` parameter.',
+        'void is only valid as a return type or generic type argument or the type of a `this` parameter.',
+      invalidVoidUnionConstituent:
+        'void is not valid as a constituent in a union type',
     },
     schema: [
       {
@@ -136,7 +139,7 @@ export default util.createRule<[Options], MessageIds>({
     ): void {
       if (parentNode.default !== node) {
         context.report({
-          messageId: 'invalidVoidNotReturnOrGeneric',
+          messageId: getNotReturnOrGenericMessageId(node),
           node,
         });
       }
@@ -218,7 +221,7 @@ export default util.createRule<[Options], MessageIds>({
             allowInGenericTypeArguments && allowAsThisParameter
               ? 'invalidVoidNotReturnOrThisParamOrGeneric'
               : allowInGenericTypeArguments
-              ? 'invalidVoidNotReturnOrGeneric'
+              ? getNotReturnOrGenericMessageId(node)
               : allowAsThisParameter
               ? 'invalidVoidNotReturnOrThisParam'
               : 'invalidVoidNotReturn',
@@ -228,3 +231,11 @@ export default util.createRule<[Options], MessageIds>({
     };
   },
 });
+
+function getNotReturnOrGenericMessageId(
+  node: TSESTree.TSVoidKeyword,
+): MessageIds {
+  return node.parent!.type === AST_NODE_TYPES.TSUnionType
+    ? 'invalidVoidUnionConstituent'
+    : 'invalidVoidNotReturnOrGeneric';
+}
diff --git a/packages/eslint-plugin/tests/rules/no-invalid-void-type.test.ts b/packages/eslint-plugin/tests/rules/no-invalid-void-type.test.ts
index 8164e85b2bd2..1a972b665be5 100644
--- a/packages/eslint-plugin/tests/rules/no-invalid-void-type.test.ts
+++ b/packages/eslint-plugin/tests/rules/no-invalid-void-type.test.ts
@@ -316,7 +316,7 @@ ruleTester.run('allowInGenericTypeArguments: true', rule, {
       code: 'type UnionType2 = string | number | void;',
       errors: [
         {
-          messageId: 'invalidVoidNotReturnOrGeneric',
+          messageId: 'invalidVoidUnionConstituent',
           line: 1,
           column: 37,
         },
@@ -326,12 +326,32 @@ ruleTester.run('allowInGenericTypeArguments: true', rule, {
       code: 'type UnionType3 = string | ((number & any) | (string | void));',
       errors: [
         {
-          messageId: 'invalidVoidNotReturnOrGeneric',
+          messageId: 'invalidVoidUnionConstituent',
           line: 1,
           column: 56,
         },
       ],
     },
+    {
+      code: 'declare function test(): number | void;',
+      errors: [
+        {
+          messageId: 'invalidVoidUnionConstituent',
+          line: 1,
+          column: 35,
+        },
+      ],
+    },
+    {
+      code: 'declare function test<T extends number | void>(): T;',
+      errors: [
+        {
+          messageId: 'invalidVoidUnionConstituent',
+          line: 1,
+          column: 42,
+        },
+      ],
+    },
     {
       code: 'type IntersectionType = string & number & void;',
       errors: [
@@ -394,7 +414,7 @@ ruleTester.run('allowInGenericTypeArguments: true', rule, {
       code: 'type invalidVoidUnion = void | Map<string, number>;',
       errors: [
         {
-          messageId: 'invalidVoidNotReturnOrGeneric',
+          messageId: 'invalidVoidUnionConstituent',
           line: 1,
           column: 25,
         },

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