Yes! You are be able to log into your account from another device. If you are only using Apple devices you're able to connect to either to Game Center or Facebook to do so, Android devices support Google Play and Facebook accounts. If you want to mix Apple and Android devices, connect your account to Facebook.
The way to do this is to download the game to your new device, start it up, tap the connect button in the initial screen, and select the same account type you linked your account to on your original device. After authenticating you're good to go!
Note: You are not able to be active on the same account on two devices at the same time.