The Avalanche traded a 2022 first-round pick and young defenseman Conor Timmins for the 31-year-old Kuemper, a source confirmed to ESPN on Wednesday.
The Avalanche also gave the Coyotes a conditional 2024 third-round draft choice.
Colorado was left desperate for a goaltender on the first day of NHL free agency, as 17 different goaltenders either received new contracts or were traded in a 24-hour span. That included Grubauer, the Avalanche's starter for three seasons who was a finalist for the Vezina Trophy last season.
The expansion Seattle Kraken signed Grubauer to a six-year deal worth $5.9 million annually.
"I don't think we expected Grubauer to get to free agency," said Seattle GM Ron Francis, "and we were fortunate enough to get him signed."
Kuemper has one year left on his contract at $4.5 million against the salary cap. The Coyotes are retaining $1 million of that to facilitate the trade, according to Sportsnet.
That left the Avalanche, a favorite to win the Stanley Cup next season, with only backup Pavel Francouz under contract for next season, a goalie who missed the entire 2020-21 season after surgery for a lower body injury.
Kuemper was one of the best -- and only -- options available on the trade market. He's entering his 10th NHL season, having played the past four seasons in Arizona where he had a 55-48-15 record with a .920 save percentage and a 2.43 goals-against average. Over the past three seasons, Kuemper has 44.1 goals saved above average, 12th among all goaltenders and right ahead of Grubauer (42.5).
Last season, Kuemper had a 10-11-3 record with a .907 save percentage.
Timmins, 22, was a second-round pick for the Avalanche in 2017. He's played 32 games in the NHL over the past two seasons with Colorado, tallying seven points. He was known as an offensive defensemen in Canadian junior hockey, but has yet to replicate that on the pro level. The Avalanche dealt from a position of strength, as they have a deep group of defensemen.
The trade gives the Coyotes two first-round picks to go along with five second-round selections in the 2022 NHL Draft. After losing goalie Antti Raanta as a free agent to Carolina and trading Kuemper, former Buffalo Sabres goalie Carter Hutton is the only goalie under contract with substantive NHL experience.