diff --git a/docs/rules/function-component-definition.md b/docs/rules/function-component-definition.md
index 5851d3baeb..f1883733cc 100644
--- a/docs/rules/function-component-definition.md
+++ b/docs/rules/function-component-definition.md
@@ -31,12 +31,13 @@ function getComponent() {
 
 ## Rule Options
 
-This rule takes an options object as a second parameter where the preferred function type for components can be specified. The first property of the options object is `"namedComponents"` which can be `"function-declaration"`, `"function-expression"`, or `"arrow-function"` and has `'function-declaration'` as its default. The second property is `"unnamedComponents"` that can be either `"function-expression"` or `"arrow-function"`, and has `'function-expression'` as its default.
+This rule takes an options object as a second parameter where the preferred function type for components can be specified. The first property of the options object is `"namedComponents"` which can be `"function-declaration"`, `"function-expression"`, `"arrow-function"`, or an array
+containing any of those and has `'function-declaration'` as its default. The second property is `"unnamedComponents"` that can be either `"function-expression"` or `"arrow-function"`, and has `'function-expression'` as its default.
 
 ```js
 ...
 "react/function-component-definition": [<enabled>, {
-  "namedComponents": "function-declaration" | "function-expression" | "arrow-function",
+  "namedComponents": "function-declaration" | "function-expression" | "arrow-function" | Array<string>,
   "unnamedComponents": "function-expression" | "arrow-function"
 }]
 ...
diff --git a/lib/rules/function-component-definition.js b/lib/rules/function-component-definition.js
index 6842b25bf2..2804188881 100644
--- a/lib/rules/function-component-definition.js
+++ b/lib/rules/function-component-definition.js
@@ -109,23 +109,44 @@ module.exports = {
 
     messages,
 
-    schema: [{
-      type: 'object',
-      properties: {
-        namedComponents: {
-          enum: ['function-declaration', 'arrow-function', 'function-expression'],
-        },
-        unnamedComponents: {
-          enum: ['arrow-function', 'function-expression'],
+    schema: [
+      {
+        type: 'object',
+        properties: {
+          namedComponents: {
+            oneOf: [
+              {
+                enum: [
+                  'function-declaration',
+                  'arrow-function',
+                  'function-expression',
+                ],
+              },
+              {
+                type: 'array',
+                items: {
+                  type: 'string',
+                  enum: [
+                    'function-declaration',
+                    'arrow-function',
+                    'function-expression',
+                  ],
+                },
+              },
+            ],
+          },
+          unnamedComponents: {
+            enum: ['arrow-function', 'function-expression'],
+          },
         },
       },
-    }],
+    ],
   },
 
   create: Components.detect((context, components) => {
     const configuration = context.options[0] || {};
 
-    const namedConfig = configuration.namedComponents || 'function-declaration';
+    const namedConfig = Array.isArray(configuration.namedComponents) ? configuration.namedComponents : [configuration.namedComponents] || ['function-declaration'];
     const unnamedConfig = configuration.unnamedComponents || 'function-expression';
 
     function getFixer(node, options) {
@@ -161,12 +182,12 @@ module.exports = {
 
       if (node.parent && node.parent.type === 'Property') return;
 
-      if (hasName(node) && namedConfig !== functionType) {
+      if (hasName(node) && !namedConfig.includes(functionType)) {
         report(node, {
-          messageId: namedConfig,
+          messageId: namedConfig[0],
           fixerOptions: {
-            type: namedConfig,
-            template: NAMED_FUNCTION_TEMPLATES[namedConfig],
+            type: namedConfig[0],
+            template: NAMED_FUNCTION_TEMPLATES[namedConfig[0]],
             range: node.type === 'FunctionDeclaration'
               ? node.range
               : node.parent.parent.range,
diff --git a/tests/lib/rules/function-component-definition.js b/tests/lib/rules/function-component-definition.js
index 47f94e0b72..3a84bcad77 100644
--- a/tests/lib/rules/function-component-definition.js
+++ b/tests/lib/rules/function-component-definition.js
@@ -78,8 +78,8 @@ ruleTester.run('function-component-definition', rule, {
       options: [{ namedComponents: 'function-declaration' }],
     },
     {
-    // shouldn't trigger this rule since functions stating with a lowercase
-    // letter are not considered components
+      // shouldn't trigger this rule since functions stating with a lowercase
+      // letter are not considered components
       code: `
         const selectAvatarByUserId = (state, id) => {
           const user = selectUserById(state, id)
@@ -89,8 +89,8 @@ ruleTester.run('function-component-definition', rule, {
       options: [{ namedComponents: 'function-declaration' }],
     },
     {
-    // shouldn't trigger this rule since functions stating with a lowercase
-    // letter are not considered components
+      // shouldn't trigger this rule since functions stating with a lowercase
+      // letter are not considered components
       code: `
         function ensureValidSourceType(sourceType: string) {
           switch (sourceType) {
@@ -346,6 +346,34 @@ ruleTester.run('function-component-definition', rule, {
       `,
       options: [{ unnamedComponents: 'function-expression' }],
     },
+
+    {
+      code: 'function Hello(props) { return <div/> }',
+      options: [{ namedComponents: ['function-declaration', 'function-expression'] }],
+    },
+    {
+      code: 'var Hello = function(props) { return <div/> }',
+      options: [{ namedComponents: ['function-declaration', 'function-expression'] }],
+    },
+    {
+      code: 'var Foo = React.memo(function Foo() { return <p/> })',
+      options: [{ namedComponents: ['function-declaration', 'function-expression'] }],
+    },
+    {
+      code: 'function Hello(props: Test) { return <p/> }',
+      options: [{ namedComponents: ['function-declaration', 'function-expression'] }],
+      features: ['types'],
+    },
+    {
+      code: 'var Hello = function(props: Test) { return <p/> }',
+      options: [{ namedComponents: ['function-expression', 'function-expression'] }],
+      features: ['types'],
+    },
+    {
+      code: 'var Hello = (props: Test) => { return <p/> }',
+      options: [{ namedComponents: ['arrow-function', 'function-expression'] }],
+      features: ['types'],
+    },
   ]),
 
   invalid: parsers.all([
@@ -879,5 +907,47 @@ ruleTester.run('function-component-definition', rule, {
       options: [{ unnamedComponents: 'arrow-function' }],
       errors: [{ messageId: 'arrow-function' }],
     },
+    {
+      code: `
+        function Hello(props) {
+          return <div/>;
+        }
+      `,
+      output: `
+        var Hello = (props) => {
+          return <div/>;
+        }
+      `,
+      options: [{ namedComponents: ['arrow-function', 'function-expression'] }],
+      errors: [{ messageId: 'arrow-function' }],
+    },
+    {
+      code: `
+        var Hello = (props) => {
+          return <div/>;
+        };
+      `,
+      output: `
+        function Hello(props) {
+          return <div/>;
+        }
+      `,
+      options: [{ namedComponents: ['function-declaration', 'function-expression'] }],
+      errors: [{ messageId: 'function-declaration' }],
+    },
+    {
+      code: `
+        var Hello = (props) => {
+          return <div/>;
+        };
+      `,
+      output: `
+        var Hello = function(props) {
+          return <div/>;
+        }
+      `,
+      options: [{ namedComponents: ['function-expression', 'function-declaration'] }],
+      errors: [{ messageId: 'function-expression' }],
+    },
   ]),
 });