"Steve (Tisch) and I both believe it is in the best interest of our franchise to move in another direction," team President John Mara said in a statement shortly after 5:30 p.m.
"We met with Joe [Monday] afternoon to discuss the state of the team," Mara added. "I met again with Joe this afternoon, and it was during that conversation I informed Joe of our decision. We appreciate Joe's efforts on behalf of the organization.
"I said before the season started that I wanted to feel good about the direction we were headed when we played our last game of the season. Unfortunately, I cannot make that statement, which is why we have made this decision.
"We will hire a general manager and that person will lead the effort to hire a new head coach."
ESPN's Josina Anderson broke the news on Twitter.
On Monday, senior vice president and general manager Dave Gettleman announced his retirement following a 35-year career in the National Football League.
Mara and Tisch said they've already begun the search for a general manager. Candidates will be announced after each interview is completed, they said.
"This will be a comprehensive search for our next general manager," Mara said. "We are looking for a person who demonstrates exceptional leadership and communication abilities, somebody who will oversee all aspects of our football operations, including player personnel, college scouting and coaching."
Tisch added: "It is an understatement to say John and I are disappointed by the lack of success we have had on the field. We are united in our commitment to find a general manager who will provide the direction necessary for us to achieve the on-field performance and results we all expect."
Click here to follow Daily Voice Bristol and receive free news updates.