Fleming, who has twice led Chennai Super Kings to the IPL title, will take charge for the 2015-16 season, replacing the out-of-contract Greg Shipperd.
Shipperd led the Stars to four consecutive semi-final appearances but have failed to reach the final.
Fleming says he will bring some fresh ideas to the side from his seven years coaching in the IPL.
"I think it's widely known the Melbourne Stars has a lot of potential to win," he says.
"With the playing squad and talent at the club, they should always be a competitive side. It's a great time to get the team - they're not too far away from achieving their goals and yet it's going to be a great challenge to get them over that final hurdle."
Fleming is already familiar with a number of side's players having coached or played against them over the years, such as David Hussey, John Hastings and Kevin Pietersen.
"There's been a lot written about Kevin, and whether or not he should be playing international cricket. I'm pretty pleased he's playing with the Stars."
"I certainly enjoyed playing against Kevin at in international level and I look forward to working with him. He's had a big impact already at the Stars and I look forward to improving on that," said Fleming.