Yes, if they both have the same OS, i.e. both are Android or iOS. The only thing you need to do is log in with your Google Play Games or Game Center account on both devices and you will have access to your game state saved on our servers.
Unfortunately, you can't play the same game on different OS i.e. iPhone and Android Tablet, because Google Play and AppStore don't share your data with each other. However, you can use it in your advantage and start playing from the very beginning on your brand new device :)