The decision to dispense with the 50-year-old ends Warzycha's long-standing association with the Crew, having spent 18 years with the club as a player and coach.
The Crew are currently eighth in the Eastern Conference and have lost seven of their last 10 games, prompting chairman Anthony Precourt to turn to Bliss to turn the team's fortunes around.
Bliss, Crew's technical director, has been set the target of steering the club into the MLS Cup play-offs in the remaining games of this season.
A statement from Precourt read: "I have been intently following this team since mid-April when we decided to explore the possibility of acquiring the Crew.
"When we came to the conclusion that we were not going to retain Robert beyond this season, it was apparent that we needed to make this change now so that we can refocus the club around Brian's leadership for the remainder of this season, as well as get the process started on finding a new head coach."
He added: "I know it's going to change the team dynamic. It's going to be a different voice. It's going to be a different perspective.
"I'm hoping and I'm very optimistic that this is going to spark the team and that we're going to make a run at the play-offs and try to get in this year."
Warzycha was promoted to the role of head coach in 2009 having previously been an assistant coach.
Bliss, a former Crew player, has held coaching positions at Kansas City Wizards and Connecticut Wolves.
