Blatt will have Drew, Jim Boylan, Bret Brielmaier and James Posey on the bench with him along with Tyronn Lue, who was named an associate head coach in June.
Drew went 15-67 in his only season in Milwaukee. He was expected to get a second year but was fired so the Bucks could hire Jason Kidd.
Drew, a former NBA player, also coached the Atlanta Hawks.
Boylan and Brielmaier both return for their second season with the Cavs.
Posey spent last season coaching Cleveland's Development League affiliate in Canton. He won league titles as a player with Miami and Boston.
Also, Phil Handy will also serve as the team's director of player development and Vitaly Potapenko has been retained as assistant director of player development.