This Babel plugin worked for me:

https://github.com/loganfsmyth/babel-plugin-transform-decorators-legacy

npm i --save-dev babel-plugin-transform-decorators-legacy

.babelrc

{
  "presets": ["es2015", "stage-0", "react"],
  "plugins": [
    ["transform-decorators-legacy"],
    // ...
  ]
}

or

Webpack

{
  test: /\.jsx?$/,
  loader: 'babel',
  query: {
    cacheDirectory: true,
    plugins: ['transform-decorators-legacy' ],
    presets: ['es2015', 'stage-0', 'react']
  }
}

React Native

With react-native you must use the babel-preset-react-native-stage-0 plugin instead.

npm i --save babel-preset-react-native-stage-0

.babelrc

{
  "presets": ["react-native-stage-0/decorator-support"]
}

Please see this question and answer for a complete explanation.