The club parted company with 25-year-old Serbian Marko Vasiljevic on Monday after just two months in charge.
Of the 10 league matches played so far, the team has won only two matches and drawn four and now place their faith in the experienced former Rwanda national team coach to rebuild it into a top outfit and challenge for trophies.
He is expected to start working on Tuesday.
Interestingly, Mbungo - who two years ago coached Gor Mahia striker Jacques Tuyisenge while at Police FC - will take charge of his first match against K'Ogalo on Saturday.
Vasiljevic on the other side was handed the mantle after his compatriot Nikola Kavazovic ditched Ingwe for South African side Free State Stars barely two weeks after penning a two year deal in the den.
Mbungo becomes the third coach at Leopards this season.