The Bulls entered the lottery with the seventh best odds for getting the top pick, which went to the Minnesota Timberwolves.
The Golden State Warriors will have the number two pick and the Charlotte Hornets received the number three overall pick.
The Bulls had a 32% chance of moving into the top four spots
The draft, originally scheduled for June, is set for Oct. 16. But nobody knows yet when the new draft picks will make their NBA debuts, since the start of the 2020-21 season is not yet determined.
The NBA had been hoping for a Dec. 1 start to the 2020-21 season, though Commissioner Adam Silver said on the ESPN telecast of that draft lottery that date now "is feeling a little bit early to me."
Unlike a year ago, when Zion Williamson was clearly going to be the first selection, there is no consensus about the No. 1 pick. Top candidates include Georgia's Anthony Edwards, Memphis' James Wiseman and LaMelo Ball - the brother of New Orleans guard Lonzo Ball.
Edwards, a 6-foot-5 guard, averaged 19.1 points in 32 games for Georgia in his lone college season. Wiseman, a 7-foot-1 center, played in only three games for Memphis and averaged 19.7 points before giving up what had been a lengthy fight with the NCAA over his eligibility. Ball, a 6-foot-7 guard, averaged 17 points in 12 games while playing in Australia's top pro league this past season.
The Bulls have picked fourth four previous times, selecting Eddy Curry in 2001, Marcus Fizer in 2000, Kelvin Ramsey in 1980 and Tom Boerwinkle in 1968.
The Associated Press contributed to this report.