The 53 year old Scot will begin work at The City Ground tomorrow and will be in charge for Saturday’s home game against Crystal Palace (kick-off 3pm).
Chairman Fawaz Al Hasawi said: “I’m delighted to welcome Alex to our Club and look forward to working with him.
“Alex took Birmingham to promotion from the Championship and has great experience of working in the Premier League.
“He’s hungry for more success and I believe he’s the man who can help us fulfil our ambition of making it to the Premier League.”
McLeish made his name as a manager in Scotland with Motherwell, Hibernian, Rangers and the Scottish national team.
He led Rangers to two Premier Division titles, as well as three Scottish League Cups and two Scottish Cups and also guided them into the last 16 of the Champions League.
He left Rangers in 2006 and after a spell away from management succeeded Walter Smith as manager of the Scottish national side the following year.
He masterminded a historic win over France in Paris during qualification for Euro 2008 as the Scots secured a play-off place but were pipped for a place in the finals by Italy.
He joined Birmingham in 2007 and guided them to promotion to the Premier League at the first time of asking in 2009.
He was named top flight Manager of the Month for December ‘09 after masterminding a 12-game unbeaten run.
In February 2011 he led The Blues to a League Cup final win over Arsenal but left St. Andrews at the end of that season. He spent last season in charge of Aston Villa.
As a player McLeish starred as a central defender in Alex Ferguson’s Aberdeen side, making almost 500 league appearances and winning the European Cup Winners’ Cup in 1982, and was capped 77 times by Scotland.