react-native-webp adds support for WebP images for react-native components.
npm install https://github.com/dbasedow/react-native-webp.git --save
rnpm link(or manually add module to your project)
You don't have to do anything other than use WebP images. This project adds a custom RCTImageDataDecoder to your project, so all react-native components should be able to use WebP files. If you are using custom components that work with UIImages directly (without using RCTImageDataDecoder) you will have to change that code.