The deal is likely to be completed as soon as Tuesday, when the Bulls are expected to waive center Tony Bradley to clear a roster spot to sign Beverley, sources tell ESPN. Bradley is expected to garner interest on the free-agent market for teams in need of a reserve center.
The Bulls want Beverley, a Chicago native who attended John Marshall High School, to bring some ferocity to the court and locker room.
Beverly spoke about the impending move on his podcast Tuesday morning.
"The Bulls have been after me the last couple years," Beverley said. "I figured I can make a playoff push with the Bulls right now and kind of pump them up a little bit. The East kind of weak, you feel me? Not to disrespect anybody from the East, but a lot of people went to the West. So I'm excited, I'm excited."
Beverley's eventual signing will help ease the loss of guard Lonzo Ball, who the Bulls shut down for the remainder of the season on Tuesday. Ball has been hampered by left knee discomfort and has not played in a game this season.
With a 26-33 record at the All-Star break, the Bulls are in 11th place in the Eastern Conference standings, two games back of the Toronto Raptors for the final play-in spot.
Beverley averaged 6.4 points, 3.1 rebounds and 2.6 assists in 45 starts for the Los Angeles Lakers this season before being dealt to the Orlando Magic at the Feb. 9 trade deadline. The Magic waived Beverley on Feb. 12 after reaching a buyout agreement, and he subsequently cleared waivers to become a free agent.