Chicago gets the earlier of Calgary's two second-round selections in the draft.
Gustafsson had a breakout season in 2018-19, with 17 goals and 43 assists, becoming one of just six defensemen in the league with 60 or more points.
But this season the 27-year-old took a step back -- at a bad time in his career. He is in the final season of a two-year contract that carries a $1.2 million cap hit.
With Brent Seabrook, Duncan Keith, Olli Maatta, Calvin de Haan and Connor Murphy all under contract through 2021-22, there was already a logjam on the blueline for Chicago. Then 19-year-old Adam Boqvist played his way onto the NHL roster.
Gustafsson had helped quarterback a productive first power-play unit for much of last season, but this year he lost that job. He had already been criticized for his defense, so losing a offensive job was another indication that he wasn't in the Blackhawks' long-term plans.
Forbort has one assist in 13 games this season, his fifth with LA.
The Flames currently hold the first wild card in the West, while the Blackhawks have faded, sitting eight points out of the second wild card.