The 52-year-old makes the move across Birmingham just five days after resigning from his post at Birmingham City, whom he could not save from relegation from the English Premier League last season.
Villa pressed ahead with the appointment despite protests from supporters and a row with the Blues.
McLeish said: "I am honoured to have this opportunity to manage a club with such a fantastic history as Aston Villa's.
"The heritage, the history of success and the tradition of Aston Villa are compelling and irresistible. The challenge for me is to try to add my own chapter."
Villa have not yet confirmed the length of McLeish's contract but have said the Scot will commence duties immediately.
The Blues were angered when it became apparent McLeish was a contender for the Villa vacancy and accused their rivals of tapping up the former Rangers and Scotland boss.
They also demanded ?£5.4million ($8.7m) in compensation to cover the remaining two years of McLeish's contract but threats to report Villa to the Premier League or take out an injunction to block the move were not carried out.
McLeish becomes Villa's third full-time manager in nine months.
Martin O'Neill resigned just five days before the 2010-11 campaign began and his successor Gerard Houllier stepped down at the end of the season for health reasons.
McLeish added: "I know that some of our fans have voiced concerns and I can understand why.
"It will be up to me to convince you that I am the right man to drive the club forward and I intend to give absolutely everything to prove that I can be a success at the club."
Source: AFP
Source: AFP