The 26-year-old defenseman, who is a restricted free agent and filed for salary arbitration on Oct. 10, scored 28 points (six goals, 22 assists) in 68 games last season. He also had 10 points (two goals, eight assists) in 22 postseason games to help New York advance to Eastern Conference Final for the first time since 1993.
Selected by the Islanders in the fourth round (No. 108) of the 2014 NHL Draft, Toews has scored 46 points (11 goals, 35 assists) in 116 regular-season games and 15 points (three goals, 12 assists) in 30 postseason games.
"Devon is a smart, two-way, puck-moving defenseman who plays 20-plus minutes a night," Avalanche general manager Joe Sakic. "He is a durable defender who is excellent in transition and we are excited to add him to our blueline."
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The Islanders did not have a second-round pick in the 2021 draft after they traded theirs to the New Jersey Devils for defenseman Andy Greene on Feb. 16.
"We did give up a good hockey player to acquire assets," Islanders general manager Lou Lamoriello said. "The arbitration was coming up, so there's a lot of circumstances that came into play in this decision.
"We would not have made this move certainly if the ice time that Devon received, we didn't have the ability to put a player into that, and Noah Dobson will certainly, we feel is ready to take the next step. We'll have to just wait and see."
NHL.com deputy managing editor Brian Compton contributed to this report