Note: This solution is old. Please refer to https://facebook.github.io/react-native/docs/images.html#background-image-via-nesting instead
Try this solution. It is officially supported. I have just tested it and works flawlessly.
var styles = StyleSheet.create({
backgroundImage: {
flex: 1,
alignSelf: 'stretch',
width: null,
}
});
And as for using it as Background image, just do the following.
<Image style={styles.backgroundImage}>
<View>
<Text>All your stuff</Text>
</View>
</Image>