The move to interview McLeish, who was unable to prevent Birmingham being relegated from the Premier League last season, resulted in protests at Villa Park this week by a number of die-hard fans.
McLeish, who faces a legal challenge from his former club over his departure, succeeds Gerard Houllier who resigned on June 1 through ill health.
"I am honoured to have this opportunity to manage a club with such a fantastic history as Aston Villa's," said McLeish, a former central defender who served Aberdeen and Scotland for many years.
"I know some of our fans have voiced concerns and I can understand why," he told the club's website.
"It will be up to me to convince you I am the right man to drive the club forward and I intend to give absolutely everything to prove I can be a success at the club."
Birmingham are unhappy at the way McLeish left his post last Sunday and stated their intention to "vigorously pursue the matter."
"We are very disappointed with how the club and its fans have been treated by Mr McLeish given the way we have supported him over the years and we are still looking into whether Aston Villa's conduct has been in line with Premier League rules," the club said on their website.
"As the club is currently enforcing its legal right with Mr McLeish, the matter is in the hands of our lawyers, and it is therefore not appropriate for the club to make any further comment at this stage."
'RIGHT MAN'
The 52-year-old McLeish established his managerial reputation at Scottish Premier League clubs Motherwell, Hibernian and Rangers before taking over as Scotland manager in January 2007.
The national team appointment did not last long as he moved to England to replace Steve Bruce at Birmingham in November of that year.
Birmingham were relegated at the end of his first season but he took them straight back up to the top flight for the 2009/10 campaign where they finished ninth, their highest position for more than half a century.
This year proved to be a mixed one as McLeish went from the highs of stunning Arsenal in the League Cup Final to the lows of a dramatic decline in league form which ended in relegation on the final day of the season.
Villa had a lacklustre season, finishing ninth, and Houllier was forced to relinquish control for the last five games of the season after he was confined to bed for eight days in April, a decade after undergoing open heart surgery.
The 63-year-old Frenchman then stepped down and Villa approached Wigan Athletic manager Roberto Martinez, among others, to fill the vacancy but the Spaniard opted to stay put and McLeish became available soon after.
"We believe we have appointed the right man for the job," Villa chief executive Paul Faulkner said.
"Unquestionably, Alex meets the criteria we set out at the beginning of our search which was based on proven Premier League experience, leadership, a hard-working ethic and, most importantly, a shared vision for Ast
