He was handed the reins of the NHL club during a news conference this afternoon, officially taking over as president and general manager.
He gets a six-year deal worth a reported $3 million annually.
The move comes after months of speculation about Burke's future.
He replaces Cliff Fletcher, who was hired as interim general manager following the firing of John Ferguson in January.
Burke spent the past three-plus seasons managing the Anaheim Ducks, leading them to a Stanley Cup title in 2007.
He stepped down from the post on Nov. 13 after declining to sign a contract extension that would take him beyond this season.
Burke's track record suggests that it shouldn't take very long for him to start putting his stamp on the team.
During previous management stops in Hartford, Vancouver and Anaheim, the 53-year-old has been unafraid to make bold moves.