The Kings will also acquire an additional fourth-round pick in 2022 if Toffoli re-signs with Vancouver.
Toffoli, 27, is set to become an unrestricted free agent after the season. In 58 games this year he has 18 goals and 34 points.
Toffoli has spent his entire eight-year career with the Kings, which included winning the Stanley Cup in 2014. His final game with the club came in a Stadium Series games on Feb. 15 against the Colorado Avalanche, where he scored all three goals in a 3-1 win.
“Tyler brings goal scoring abilities and is good in battles,” Canucks general manager Jim Benning said in a statement. “He has great offensive instincts and experience playing in high pressure, meaningful games. We look forward to adding his skill and strength to the line-up.”
Schaller, 29, has six points in 51 games for the Canucks this season, his second in Vancouver. He also is due to become an unrestricted free agent at the end of the season.
Madden, 20, was a third-round pick by the Canucks in 2018. This season, with Northeastern in the NCAA, he has 19 goals and 37 points in 27 games.
This is the second trade the Kings have made in recent weeks ahead of the Feb. 24 trade deadline. On Feb. 5, the club sent goalie Jack Campbell and forward Kyle Clifford to the Toronto Maple Leafs for forward Trevor Moore and two third-round picks.
Kings general manager Rob Blake said on a conference call that talks on Toffoli really heated up over the weekend but said it was difficult to trade a player that has been with the team for a long time.
“We’ve always understand there’s a certain (price) that Tyler, if he was to be moved, would have to bring,” Blake said. “When you look at the possible deals that you may have to make and you put a range on what the return would be, I think my feeling is once that is met, you move forward on it.”
The Canucks also announced Monday that winger Brock Boeser will miss at least three more weeks with a a rib cartilage fracture and forward Micheal Ferland has been shut down for the season due to a concussion.
Entering Tuesday, the Canucks sit third in the Pacific Division — but the division’s top five teams are separated by just two points.
Toffoli is expected to be at practice with the Canucks on Tuesday. The team returns to action Wednesday at home against the Minnesota Wild.