Crawford directed the Stars to a 79-60-25 record in his two seasons with the NHL club.
"I would like to thank Marc for the hard work he provided to the Dallas Stars over the last two seasons," General Manager Joe Nieuwendyk said. "We wish him the best in the future."
Crawford previously had coached the Quebec Nordiques/Colorado Avalanche, Vancouver Canucks and Los Angeles Kings. He won the Stanley Cup with the Avalanche in 1996.