The deal also will send Anthony Randolph to Chicago and a future second-round pick to Denver.
The Bulls were high on the former Creighton star all season, scouting him a number of times. They were also looking for a trade partner for the 16th and 19th picks to shave money off next year's salary cap.
Is that a good sign for the Bulls' free-agent hopes this summer?
While the Bulls pursue free agent Carmelo Anthony, getting McDermott addresses one of their biggest needs: shooting and scoring.
As a team, the Bulls shot 42 percent from the field and 33.3 percent on 3-pointers last year. They were the lowest-scoring team in the NBA, averaging 93.7 points per game without Derrick Rose for all but 10 games.
"I think I can provide some outside shooting right from the get-go, be able to come off screens and play off their superstars," McDermott said.
McDermott was the consensus college player of the year during his senior season, averaging 26.7 points, shooting 52.6 percent from the field and 45 percent from 3-point range.
"He handled his college career great," Bulls coach Tom Thibodeau said. "There was a lot of pressure on him and he met all those expectations. I had an opportunity to be around him with USA Basketball last summer, and he more than held his own in that setting."
McDermott is the fifth-highest scorer in Division I history with 3,150 points, and he is a career .458 shooter from 3-point range.
McDermott could play the post in college, and was measured at 6-foot-7-3/4 with shoes on at the NBA draft combine.
"If you're just viewing him strictly as a shooter, you're not casting him in the proper light," Thibodeau said. "Because he's a lot more than that. We think he's a complete player. We think he's capable of playing very good defense."
Information from ESPN's Jeff Goodman was used in this report.