Burke was announced as winner of the John R. Wooden Award, which is administered by the Los Angeles Athletic Club, and the Oscar Robertson Trophy, given by the U.S. Basketball Writers Association.
Burke and the Wolverines (30-7) are in the NCAA Tournament's Final Four, taking on Syracuse Saturday.
The Michigan star was also voted the Big Ten Player of the Year after leading his team with averages of 18.8 points and 6.8 assists a game.
A nationwide panel of college basketball media members voted on the Wooden Award, with Burke totaling 2,808 points, 90 more than Indiana's Victor Oladipo. Creighton's Doug McDermott (2,344) was third and Georgetown's Otto Porter (2,144) finished fourth.
Burke is the first Michigan player to win the Wooden Award, which was first given in 1977, and the second Wolverine to get the basketball writers' trophy, joining Cazzie Russell, the 1966 winner.
The honor is determined by a vote of more than 900 members of the USBWA. The association didn't release a breakdown of the voting.
Kentucky freshman Anthony Davis won both awards last year.