The 35-year-old, the Republic of Ireland's most-capped international, last night signed a five-year contract to become McLeish's first signing at Villa Park.
He had been frozen out under City boss Roberto Mancini as England international Joe Hart made the position between the posts his own, and former Birmingham manager made him his prime target to replace the departed Brad Friedel.
Villan of the piece: McLeish is expecting great things from his new keeper
'Shay has come here probably with something of a point to prove and that won't do any harm at all,' McLeish told the club's website.
'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.
'He's a real competitor and a world-class keeper and I'm delighted he's the first signing I've made at Villa.'
Given started his career as a youngster at Celtic, who he had been linked with all this summer, before moving on to Blackburn and Newcastle.
His consistently impressive performances at St James' Park earned him a ?7million move to City in the 2009 winter transfer window but despite maintaining his form, he was eventually overtaken in the pecking order by Hart.
Given has taken a 25 per cent pay cut from the ?80,000-a-week he earned at Eastlands in exchange for the longer deal.
It never rains, but it pours: Given was forced into the sidelines at City after the emergence of Joe Hart
He said: 'Aston Villa is a huge club and I'm really excited to be joining. 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. It's also a new challenge and one I'm eager to embrace.'
'Everyoneknows that I didn't play enough football last season, so I'm really pleased that I'll be able to put that right here,' Given said.
'They're a good bunch of lads, very talented and I know several of them already which will help. Obviously, I'm also excited to be working with Alex McLeish and it's going 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 to impress the Aston Villa supporters with my performances and I can't wait really to get started.'
The signing of Given is expected to be followed by further arrivals as McLeish looks to find replacements for Ashley Young and Stewart Downing, who have made big-money moves to Manchester United and Liverpool respectively.
The club have already had a bid for Wigan winger Charles N'Zogbia refused but are expected to go back with an improved offer while they have also been heavily linked with Tottenham defender Alan Hutton and West Ham's England midfielder Scott Parker.
Filling the gaps: McLeish is chasing a number of replacements following the departures of key players
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