Dixon, 50, played for the Horned Frogs from 1984-87.
Dixon took over as the head coach at Pittsburgh in 2003 after Ben Howland left for UCLA. He has been the Panthers head coach for the past 13 seasons -- and has gone to the NCAA tournament 11 times.
However, the program hasn't been nearly as relevant nationally since making the move from the Big East to the ACC three years ago. The Panthers have not reached the Sweet 16 since 2009 and were eliminated from this year's tournament after a first-round loss to Wisconsin.
Dixon takes over for Trent Johnson, who was fired last week.
TCU was 59-79 overall under Johnson. The school made the transition from the Mountain West to the Big 12 prior to Johnson's first season with the Horned Frogs. Before Johnson, Jim Christian was 56-73 in his four seasons with the program.
The last time the Horned Frogs were in the NCAA tournament was in 1998 under Dennis Davis.