The 24-year-old will replace injured Sri Lankan fast bowler Lasith Malinga, who is recovering from a knee injury which he picked during the CB Series in Australia.
Mumbai Indians coach Lalchand Rajput confirmed the decision.
''Bravo was the unanimous choice of the few names discussed by the team think-tank,'' Rajput was qouted as saying by Cricinfo.
''The decision to pick Bravo was a collective decision,'' he added. ''We got a report that his recovery might take a further two to three weeks. So we decided to have a back-up.'' South African pace bowler Charl Langeveldt's name was also discussed, but Bravo was selected by virtue of being an allrounder.
''We wanted an allrounder and not another regular bowler''' Rajput said. Bravo will be the fourth West Indies player to feature in the IPL joining Shivnaraine Chanderpaul, Chris Gayle and Ramnaresh Sarwan.
Meanwhile, Bravo would only be available for short period before he returns home for the Australia series but the Mumbai team management felt they could extract the most out of him before he heads back.
Mumbai start their campaign against the Bangalore Royal Challengers at home and by May 14 they would've played eight of their 14 encounters.
''We know he would be returning on May 15 but by then we would have played most of our games,'' the coach said.