It's a two-year, $40 million deal, league sources told ESPN.
The agreement was consummated Saturday, moments after Milwaukee Bucks general manager Jon Horst removed the qualifying offer on the restricted free agent and allowed him to become unrestricted.
The Bucks weren't going to match a Bulls offer sheet, and the deal -- brokered with Parker's agent Mark Bartelstein -- allowed a good-faith gesture for Parker to sign a shorter deal with the Bulls.
"We really love Jabari and wanted to work with him on this, because we weren't going to match an offer sheet," Horst told ESPN.
The second year of the deal is a team option, league sources said, which lowers the risk on Chicago based on Parker's two ACL injuries and gives both sides the flexibility to turn a short-term relationship into a long-term deal should Parker stay healthy and productive next season.
Bartelstein needed the Bucks to rescind the qualifying offer because an offer sheet doesn't allow for an option by either side. For Bartelstein and Parker, a $20 million guarantee after the past injuries and an uneven final season with Milwaukee is the best possible outcome to the choppy waters of restricted free agency.
Parker, 23, will return to Chicago, where he was the No. 1 recruit in America out of Simeon High School in 2013.
The Bulls are banking on revitalizing Parker's career, restoring him to top condition and fulfilling his promise as the No. 2 overall pick in the 2014 NBA draft.
The Bulls plan to use Parker largely as a small forward.
Parker has suffered two ACL tears to his left knee in his career. He had his best season in 2016-17 -- averaging 20.1 points, 6.2 rebounds and 2.8 assists in 51 games before suffering another knee injury.