Terms of the deal involving the 6-foot-8 forward from Creighton weren't released.
The Bulls acquired 22-year-old McDermott after Denver drafted him with the 11th overall pick, then quickly traded him to Chicago.
As a Creighton senior last season, McDermott averaged a nation-leading 26.7 points, becoming one of eight players in NCAA history to score more than 3,000 career points.
The Bulls also announced Tuesday's signing of free-agent guard Aaron Brooks. The 6-foot, six-year NBA veteran last season averaged 9 points while splitting time with Denver and Houston. Terms were not disclosed.