In what could be the beginning of a big shakeup in Denver, the Broncos and coach John Fox agreed to part ways Monday — a day after they were eliminated from the playoffs by the Indianapolis Colts.

“John Fox and I met for more than an hour on Monday afternoon to discuss the 2014 season and our goals for the future,” team president John Elway said. “During our open and candid conversation, it became clear that it was best for both the Denver Broncos and Coach Fox to move on and make this change.

“On behalf of the Broncos, I sincerely thank John for his many contributions during his four seasons as head coach. He helped establish a positive, winning culture for this team and deserves a lot of credit for the Broncos’ turnaround.”

The news was first reported by Jay Glazer of FOX Sports.

Fox leaves the Broncos with a .719 winning percentage, the best in franchise history. In four seasons, he went 46-18 — thanks largely to the presence of quarterback Peyton Manning.

However, the Broncos were bounced from the divisional round by the Indianapolis Colts on Sunday, losing 24-13. It was the second time in three years Fox’s Broncos had been knocked out in their first playoff game. In between, they reached the Super Bowl, where they were blown out 43-8 by the Seattle Seahawks.

Elway reportedly insisted on Sunday that Fox would return, despite speculation that Fox could be gone if the Broncos were eliminated in the first game again.

Fox said after the divisional playoff loss to the Colts, “I’ve seen all kind of reports in the past. I’m sure I’ll see some moving forward. I don’t make those decisions, I don’t control that. My intentions are to be a Denver Bronco and have been since I got here. It’s not about me; it’s about this football team.”

Fox is the ninth coach in NFL history to not return to his team after a 12-win season, according to Elias Sports.

Speculation began last week that a Broncos loss could lead to a promotion for Adam Gase, who is a candidate for multiple head-coaching positions elsewhere. Defensive coordinator Jack Del Rio is also interviewing to be a head coach again, including with the Oakland Raiders.

“While we have made significant progress under Coach Fox, there is still work to be done,” Elway said Monday. “I believe this change at the head coaching position will be in the best interest of our long-term goal, which from Day 1 has been to win world championships.

“Our organization is fully dedicated to reaching Pat Bowlen’s high standards for his team as we begin the process of finding the next head coach to lead the Denver Broncos.”

Fox said, “I had a productive visit with John Elway this afternoon in which we were both very honest about our time together and how to best move forward. After this discussion, John and I mutually agreed that the timing was right for this decision.

“Although we came up short of our ultimate goal, I am proud of our team’s many accomplishments during these last four years. I truly appreciate all of the hard work put in by every player, coach and staff member within this organization.

“It was an honor to coach the Denver Broncos, a first-class franchise with great fans and a winning tradition. I am thankful to John, Mr. Bowlen and Joe Ellis for allowing me and my family to be part of this team and community.

“I am eager to continue my coaching career and look forward to the opportunities that lie ahead.”

Denver players apparently had no idea the split was coming.

Asked what Fox’s final message to the team was in their season-ending meeting Monday, cornerback Chris Harris said, “Just that he appreciated everybody’s efforts. He loved us. And everybody just be smart in the offseason and make sure you take care of your body to be ready to come back ready to roll when OTAs start.”

With the Buffalo Bills hiring Rex Ryan, there are now six teams looking for coaches: the Broncos, Atlanta Falcons, Chicago Bears, New York Jets, Oakland Raiders and San Francisco 49ers. Fox, who has taken two teams to the Super Bowl in 13 years as a head coach, would figure to be high on the list of some of those teams.

The Bears could have interest in Fox in a search being headed by Ernie Accorsi, former general manager of the New York Giants, where Fox coached.

Fox could be the first of several departures from the Broncos. Manning is weighing his future as well, Gase is reportedly the favorite of the San Francisco 49ers and Del Rio in Oakland. The Broncos have 17 free agents.

After the game Sunday, Manning said, “My mindset right now is just disappointment after today’s game. I kind of need to process this game and we’ll meet tomorrow, kind of need to process this game, so I’m disappointed right now.”

Asked again if he plans to play in 2015, Manning was noncommittal.

“Yeah, I guess I just can’t give that simple answer. I’m processing it. I can’t say that. I could not say that,” he said.