Boucher shocked the cricketing world earlier this week when he announced that he would be stepping down as South Africa's coach after the T20 World Cup that gets underway in Australia next month.
The former wicketkeeper's contract with the national side was due to expire at the 50-over World Cup that is due to be played in India next year.
"It's a pleasure to welcome Mark Boucher to Mumbai Indians. With his proven expertise on the field and off it as a coach guiding his team to numerous victories, Mark will add immense value to MI and take forward its legacy," Mumbai chairperson, Akash. M. Ambani, said.
Mumbai is the most successful team in the history of the IPL with five titles but the change in coach comes after they finished dead last this year, only winning four of 14 matches.
Boucher takes over the coaching reins from Sri Lanka legend Mahela Jayawardene, who has been promoted to the franchise's global head of performance.
"Their history and achievements as a franchise clearly put them up there as one of the most successful sporting franchises in all of world sport," Boucher said.
"I look forward to the challenge and respect the need for results. It's a strong unit with great leadership and players. I look forward to adding value to this dynamic unit."