Stewart will handle day-to-day operations for the program until a permanent replacement is hired.
Stewart served as an assistant under Robinson at Brown from 2006 to 2008 and for the past six seasons as an associate head coach at Oregon State. His only previous head coaching experience was at a junior college in Wyoming.
Robinson was dismissed on May 5 after posting a 93-104 record, including 39-69 in the Pac-12, in his six seasons with the Beavers.
Former UCLA coach Ben Howland, a leading candidate for the job, withdrew from consideration on Monday. With Howland out of the running, that leaves Arizona assistant Damon Stoudamire as a prime contender for the position. Stoudamire is a Portland, Ore., native.