Assistant coaches Jacques Cloutier and Dave Barr, goaltender coach Jeff Hackett and video coordinator P.J. DeLuca also were fired.
"I look forward to the challenge," Sherman said. "We all know the task ahead and we need to get to work. There are a lot of things to be done here. We are looking towards the future with a lot of optimism."
Granato's expected firing came after Hall of Fame goaltender Patrick Roy was offered the head coaching position last month, but declined, citing family reasons.
With its 32-45-5 record last season, Colorado finished with the worst record in the Western Conference.
The firing of General Manager Francois Giguere on April 13 was the first move in the team's offseason shakeup.
Former NHL goaltender Craig Billington was named vice president of hockey operations/assistant general manager and David Oliver director of player development.