Given, 35, had been out of favour at Manchester City since the rise to prominence of England No 1 Joe Hart.
And having been linked with a number of clubs, Alex McLeish has made the Republic of Ireland international his first signing as Villa boss.
On the move: Shay Given has left Manchester City to sign for Aston Villa
'Aston Villa is a huge football club and I'm really excited to be joining,' Given said. 'I'm looking forward to training and playing with the players here. They're a good bunch of lads, very talented and I knowseveral of them already which will help.
'Everyone knows that I didn't play enough football last season, so I'm really pleased that I'll be able to put that right here. Hopefully, this move will get me back to where I was before in the Premier League, which is where every player wants to be playing.
'Obviously, I'm also excited to be working with Alex McLeish and it'sgoing to be a fresh start for everybody at the club this season.
'It's also a new challenge and one I'm eager to embrace. My aim is toimpress the Aston Villa supporters with my performances and I can't wait really to get started.'
Villa manager Alex McLeish said: 'Shay has come here probably with something of a point to prove and that won't do any harm at all.
'Everybody who has watched him perform over many years in the PremierLeague will know his pedigree, so we believe we have secured the services of one of the best goalkeepers in the business.
Safe hands: Given is considered one of the best goalkeepers in the Premier League
'He's a real competitor and a world-class keeper and I'm delighted he's the first signing I've made at Villa.'
Earlier, defender Richard Dunne welcomed his international team-mate's arrival.
He said: 'I spoke to him earlier in the week, he just wanted to get here and get started,'
'Hewas frustrated over the way things have gone over the last year, I think he just wants to get playing again and he'll be looking forward toit.
'I spoke to him on Friday when he got here and I think he was surprised about how good the facilities and the setup are here at Bodymoor.
'I think it's a good opportunity for Shay to get back to playing football and I think it's one he's really looking forward to.'
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