Heaton made 19 Premier League appearances last season as Burnley avoided relegation.
Last week Villa confirmed the arrivals of Egypt international winger Trezeguet for £8.75m and Manchester City midfielder Douglas Luiz for £15m.
Heaton's arrival takes Villa's summer spending beyond £110m.
He said: "There's momentum here – you could see that from afar.
"This club got the ball rolling last season and it turned into a huge success story in the second half of the campaign.
"To gain promotion was absolutely brilliant.
"It's been a busy window so far – a lot of signings. But it needed to happen with a lot of players having also left the club.
"The majority of the signings are young, hungry and athletic. It's a really exciting time for Aston Villa and I'm delighted to be a part of that.
"Hopefully, I'll bring a bit of experience to it."