Boedker, 26, won an Ontario Hockey League championship with Kitchener coached by DeBoer.
"He's one of those players you coach over your career where he makes an impression both as a player, but also as a person," DeBoer said. "I understand what he can do. He has some untapped upside that we haven't seen yet, and [I'm] real excited to get him and work with him again."
Boedker was the eighth player taken in the 2008 NHL Draft, was a regular with the Phoenix Coyotes as an 18-year-old, and has played eight seasons in the NHL. All but the last six weeks of the 2015-16 season was spent with the Coyotes, who traded him to the Colorado Avalanche prior to the 2016 NHL Trade Deadline.
"Mikkel's tremendous speed is his best attribute and he has the ability to back off defenders with his combination of quickness and soft hands," general manager Doug Wilson told the Sharks website. "His creativity and puck-handling abilities make him a threat in the transition game and he is a positive contributor in all three zones. We think he will thrive with our group and look forward to him joining our team."
Boedker had 12 points (four goals, eight assists) in 18 games with the Avalanche, where he spent much of his time on a line with Nathan MacKinnon. Boedker's best season was in 2013-14, when he had 19 goals and 51 points. Including his time with the Coyotes, he finished last season with 17 goals and 51 points. Boedker has 84 goals and 141 assists in 463 NHL games.
"I think [speed is] something my game is built on," Boedker said. "I play fast, and hopefully I can get some good chemistry with the guys that are there now."
Before being traded, Boedker reportedly turned down a five-year contract offer from the Coyotes, who then opted to trade him to the Avalanche for Kyle Wood and the 53rd pick in the 2016 NHL Draft (as compensation for unsigned forward Conner Bleackley, who was included in the trade).
Boedker, who can play on either wing, had 51 points in two of his past three seasons (as well as 28 in 45 games during 2014-15, when he missed time with injuries).