Bruce has been out of work since leaving Hull in July over a lack of money available for transfers, despite only securing promotion with the Tigers two months before.
The 55-year-old was interviewed for the England manager’s job before Sam Allardyce took the role but was not in the running after the former West Ham boss left the role only 69 days later.
Di Matteo left Villa 19th in the Championship with only one win and 10 points from 11 games, despite spending over £50m in the summer transfer window.
Bruce said: “It’s a wonderful opportunity. It is one of the big clubs of this country. To be given the opportunity to manage it is terrific.
“I relish the challenge of trying to take the Club where it wants to go and needs to be – and try to turn around the misfortune we seem to have had over the past few years. I am absolutely delighted to have been given the chance. I hope I can do my stuff.”
The man who appointed him, owner Dr Tony Xia, said: “I’m delighted to welcome Steve to the football Club. With his track record, not only at leading teams to promotion from the Championship but also vast experience in the Premier League, I believe we have secured the services of an excellent manager.
“I have had good conversations with Steve and we look forward to working with him.”
Bruce has had spells at the likes of Sunderland, Wigan and Crystal Palace and been promoted to the Premier League four times in his career, twice with Hull and twice with Villa’s main rivals Birmingham City.
His first game in charge will be Saturday’s game at Villa Park with midland rivals Wolves.