Gruden became the Bucs' coach in 2002, when he was 39. His first team in Tampa won the Super Bowl, making him the youngest coach to do so.
The Buccaneers ended this season with four straight losses, missing the playoffs.
Allen became GM in 2004.
"We will be forever grateful to Jon for bringing us the Super Bowl title, and we thank Bruce for his contributions to our franchise," Joel Glazer, Bucs' co-chairman said. "However, after careful consideration, we feel that this decision is in the best interest of our organization moving forward."
Gruden's overall record with Tampa Bay was 57-55. He previously coached the Oakland Raiders for four seasons.
Allen also came to the Bucs from Oakland, where he was general manager for nine years.