The 35-year-old Given had slipped behind England's Joe Hart in the pecking order at City and played only a handful of first-team matches last season.
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"Aston Villa is a huge football club and I'm really excited to be joining," Given told the club's website.
"I'm looking forward to training and playing with the players here. They're a good bunch of lads, very talented and I know several of them already which will help."
Given made his name during 12 years at Newcastle United in which he made over 400 appearances before joining City in 2009 for around six million pounds.
Villa, whose first-choice keeper Brad Friedel moved to Tottenham Hotspur at the end of last season, paid around 3.5 million pounds for Given, according to newspaper reports.
Given, Ireland's most capped player with 113 international appearances, became Villa manager Alex McLeish's first signing since taking over last month.
"Everybody who has watched him perform over many years in the Premier League will know his pedigree, so we believe we have secured the services of one of the best goalkeepers in the business," McLeish said.
