As of react-scripts 2.10 you can add TypeScript to an existing project or when creating a new project.
existing project
yarn add typescript @types/node @types/react @types/react-dom @types/jest --dev
…then rename your .js files to .tsx
new project
yarn create react-app my-app --template typescript
You can read more in the docs.
If you are having trouble, the following from the troubleshooting section of the docs might help:
Troubleshooting
If your project is not created with TypeScript enabled, npx may be
using a cached version of create-react-app. Remove previously
installed versions with npm uninstall -g create-react-app or yarn
global remove create-react-app (see #6119).