"During his time in India, John was instrumental in India's rise up in the international table including finishing finalist in the 2003 World Cup. In the relatively brief period he had been in charge of the Black Caps, the Kiwis improved upon its performance reaching the semi-finals of the last World Cup," a release from Mumbai Indians said.
It said Robin Singh, who was the coach of the side last season, will continue to be associated with the team.
"Robin Singh will continue to lend his services to Mumbai Indians," the release said.
Commenting on Wright's appointment, Mumbai Indians owner Nita Ambani said, "It's a great pleasure to have John on board with Mumbai Indians. John is immensely respected and I am sure his cricketing knowledge and experience will be of enormous help."