McLeish, who resigned as manager of Blues last weekend, has been named as replacement to Gerard Houllier.
"I am honoured to have this opportunity to manage a club with such a fantastic history as Aston Villa's," McLeish said.
"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.
"Since first becoming a manager at Motherwell, my desire to succeed and my energy and drive have never waned. My objective is to impart that drive and will to win to the players and fans of Aston Villa.
"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."
Blues are expected to pursue a compensation claim against Villa's approach of their former manager who has signed a three-year contract at Villa Park.