JSPM

// Within your render function, assuming you have a file called
// "background.mp4" in your project. You can include multiple videos
// on a single screen if you like.
<Video source={{uri: "background"}} // Can be a URL or a local file.
       rate={1.0}                   // 0 is paused, 1 is normal.
       volume={1.0}                 // 0 is muted, 1 is normal.
       muted={false}                // Mutes the audio entirely.
       paused={false}               // Pauses playback entirely.
       resizeMode="cover"           // Fill the whole screen at aspect ratio.
       repeat={true}                // Repeat forever.
       onLoad={this.setDuration}    // Callback when video loads
       onProgress={this.setTime}    // Callback every ~250ms with currentTime
       onEnd={this.onEnd}           // Callback when playback finishes
       style={styles.backgroundVideo} />

// Later on in your styles..
var styles = Stylesheet.create({
  backgroundVideo: {
    position: 'absolute',
    top: 0,
    left: 0,
    bottom: 0,
    right: 0,
  },
});