The pick is the Miami Heat's first-round selection this year, which is owned by the Raptors.
Johnson was selected in the first round of the 2009 draft by the Bulls out of Wake Forest, but the 6-foot-9 small forward has averaged career totals of just 3.8 points and 1.9 rebounds per game.
"It [stinks]," Bulls center Joakim Noah said. "I consider J.J. a little brother. But he wasn't playing a lot, and I wish him nothing but the best. And I hope that he gets an opportunity to get out there on the court and show what kind of player he is."
The Bulls face the Raptors on Wednesday.
ESPN The Magazine's Ric Bucher first reported the move.
With the cap space created by dealing Johnson to Toronto, Chicago could now absorb the $2.9 million contract of Cleveland's Anthony Parker -- one of their top trade targets for weeks -- without having to part with any players. It's believed that the Cavaliers would expect at least one future first-round pick in such a swap, but the Bulls are armed with an extra first-rounder thanks to the Johnson deal.
Houston's Courtney Lee, who's making a mere $1.4 million, is another longstanding Bulls target.
But sources briefed on Chicago's thinking told ESPN.com's Marc Stein on Tuesday night that the Bulls have not yet abandoned hope of striking a deal for Memphis' O.J. Mayo, even though Mayo's $4.5 million salary would not fit into that cap space.
The Bulls appear to be trying to stockpile assets, such as the first-rounder acquired from the Raptors, for at least one more deal before Thursday's 3 p.m. trading deadline. Yet ESPN.com reported earlier this month that the Grizzlies are reluctant to trade Mayo now in the midst of his troubled season, knowing that Mayo's recent 10-game drug suspension and a fight on the team plane with teammate Tony Allen would make it hard for them to get good value for the No. 3 overall pick from the 2008 draft.
Another potential roadblock for any team interested in Mayo is the recent shoulder injury suffered by Grizzlies swingman Rudy Gay, who is expected to miss up to a month and could thus prompt Memphis to reject offers for Mayo that might have been accepted before the injury.
ESPN.com's Marc Stein and ESPNChicago.com's Nick Friedell contributed to this report.