The CFL club issued a statement Wednesday saying Bauer stepped down because of "ownership restructuring."
The NHL's Calgary Flames increased their stake in the football team from five per cent to a majority last year.
“Lyle’s decision to leave was based primarily on a significant change in roles and responsibilities given the benefits of new ownership synergy and infrastructure efficiency,” Stampeders co-chairman John Forzani said in a statement.
Bauer will act as a consultant during the transition of executives, the Stampeders said.
“The team is in good hands to carry on our commitment to solid community ownership and high-performance football,” Bauer said in the same statement.
The former CFL offensive lineman became president of the Stampeders in 2010 after nine years in the Winnipeg Blue Bombers organization.