The Irish international, 26, follows Idrissa Gueye out the door after signing a five-year deal at Newcastle.
The Toon triggered a £5m release clause in his contract.
Clark has spent his entire career at Villa but obviously feels Newcastle are a better bet to bounce back to the top flight.
He said: “Importantly, it is a club that is moving in the right direction and pushing for the right things, so I’m really excited to now be a part of that.”
Newcastle have also completed the £5m capture of Hull midfielder Mo Diame.