The Blackhawks receive a first and second-round pick in exchange, along with forward Marty Reasoner, winger Joseph Crabb and prospect Jeremy Morin.
Chicago have been forced to part with some of their players due to salary cap issues and lose Byfuglien after he netted five game-winning goals in the post-season.
"It is what it is. It's part of the job," Byfuglien told a local Chicago radio station. "You're not going to stick in one spot the whole time, so I've got to go."
(Reporting by Jahmal Corner in Los Angeles; Editing by Ian Ransom)