Thirty-nine-year-old Jayawardene will succeed former Australian captain Ricky Ponting whose two-year contract has ended.
"Jayawardene is an astute figure in the modern era of cricket. He is a perfect role model for the young Mumbai Indians squad," Mumbai Indians owner Nita Ambani said a statement.
Jayawardene, who retired from international competition last year, was part of the 2014 national squad that won the World Twenty 20 tournament.
"I am very excited by the appointment and glad that the Mumbai Indians management appreciated my presentation and ideas," Jayawardene said.
The IPL is the most popular domestic league in the world but has been plagued by controversies since its inception in 2008, with corruption and match-fixing cases often taking centre stage.
Original source: Mumbai Indians name Jayawardene as head coach