Synchronized state variables are implemented using Twilio Sync as a cloud storage back end in React applications. A custom hook called `useSyncState()` is created, which provides transparent synchronization across all running instances of the application. The hook uses the `SyncProvider` component to manage the Twilio Sync client instance and obtain access tokens from the Express backend server. The `useSyncState()` hook allows for synchronized state management, enabling updates in all instances of the application without requiring explicit manual syncing.