diff --git a/src/components/Provider.js b/src/components/Provider.js
index f78e25e65..38d70879f 100644
--- a/src/components/Provider.js
+++ b/src/components/Provider.js
@@ -1,8 +1,10 @@
-import { Component, Children } from 'react'
+import React, { Component, Children } from 'react'
 import PropTypes from 'prop-types'
 import { storeShape, subscriptionShape } from '../utils/PropTypes'
 import warning from '../utils/warning'
 
+const prefixUnsafeLifecycleMethods = parseFloat(React.version) >= 16.3
+
 let didWarnAboutReceivingStore = false
 function warnAboutReceivingStore() {
   if (didWarnAboutReceivingStore) {
@@ -38,7 +40,11 @@ export function createProvider(storeKey = 'store') {
     }
 
     if (process.env.NODE_ENV !== 'production') {
-      Provider.prototype.componentWillReceiveProps = function (nextProps) {
+      // Use UNSAFE_ event name where supported
+      const eventName = prefixUnsafeLifecycleMethods
+        ? 'UNSAFE_componentWillReceiveProps'
+        : 'componentWillReceiveProps'
+      Provider.prototype[eventName] = function (nextProps) {
         if (this[storeKey] !== nextProps.store) {
           warnAboutReceivingStore()
         }
diff --git a/src/components/connectAdvanced.js b/src/components/connectAdvanced.js
index 00ab7683c..9222f1645 100644
--- a/src/components/connectAdvanced.js
+++ b/src/components/connectAdvanced.js
@@ -1,11 +1,13 @@
 import hoistStatics from 'hoist-non-react-statics'
 import invariant from 'invariant'
-import { Component, createElement } from 'react'
+import React, { Component, createElement } from 'react'
 import { isValidElementType } from 'react-is'
 
 import Subscription from '../utils/Subscription'
 import { storeShape, subscriptionShape } from '../utils/PropTypes'
 
+const prefixUnsafeLifecycleMethods = parseFloat(React.version) >= 16.3
+
 let hotReloadingVersion = 0
 const dummyState = {}
 function noop() {}
@@ -160,6 +162,7 @@ export default function connectAdvanced(
         if (this.selector.shouldComponentUpdate) this.forceUpdate()
       }
 
+      // Note: this is renamed below to the UNSAFE_ version in React >=16.3.0
       componentWillReceiveProps(nextProps) {
         this.selector.run(nextProps)
       }
@@ -262,6 +265,12 @@ export default function connectAdvanced(
       }
     }
 
+    if (prefixUnsafeLifecycleMethods) {
+      // Use UNSAFE_ event name where supported
+      Connect.UNSAFE_componentWillReceiveProps = Connect.componentWillReceiveProps
+      delete Connect.componentWillReceiveProps
+    }
+
     /* eslint-enable react/no-deprecated */
 
     Connect.WrappedComponent = WrappedComponent