Jack Parker is an institution at Boston University

Sometimes a college coach doesn’t simply work at an institution of higher learning. He becomes an institution himself. That’s Boston University hockey coach Jack Parker, who formally announced Monday he’s putting away the whistle at the end of the season.

In his 40th season as the bench boss on Commonwealth Avenue, Parker is that rare breed of coach who has become synonymous with and inseparable from his university, like Paul “Bear” Bryant (Alabama), John Wooden (UCLA), Dean Smith (North Carolina), or Mike Krzyzewski (Duke).

He is a coaching treasure who endured the tragic paralysis of Travis Roy with grace and continuing compassion as if it were his own son. He provided four of the players for the “Miracle on Ice” 1980 US Olympic team. He turned down the opportunity to coach the Bruins — twice — to stay at his alma mater.

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Parker’s contributions to BU can’t be measured solely in wins (894 and counting), Beanpot titles (21), national championships (three), and NHL players (dozens) because his influence on the school transcends the dimensions of a hockey rink. Those who never laced up a single skate for BU, but have been associated with the university are the beneficiaries of Parker’s legacy.

The transformation of BU can be traced to two driving forces. One is the late John Silber, the domineering former president and chancellor who ruled the school with an iron fist. The other is Jackie Parker, the kid from Somerville and Catholic Memorial who gave a diverse and divided campus a unifying force to rally behind on the ice.

Even if you’re an academic whose idea of a power play is the French Revolution and you attended BU you still probably know who Parker is.

Save for one season he spent coaching at Medford High right out of college, Parker has spent nearly all of the last five decades as a player, assistant coach, or head coach at BU.

“It’s time,” said Parker, who celebrated his 68th birthday Monday. “I’ve been a coach here for 44 years. I was a player here before that. For 48 out of the last 49 years I’ve been reporting to duty for BU hockey, and that’s enough.”

It was fitting that Parker’s announcement came inside Agganis Arena, the state-of-the-art ice palace that is The House that Jack Built.

Flanked by athletic director Mike Lynch and school president Dr. Robert A. Brown, Parker was charming and witty, playing to an audience packed with former players, including Olympic legend Mike Eruzione.

He held court as the King of BU athletics, even if his reign was coming to an end.

“Yeah, it will definitely be strange,” said former Terrier Mike Grier. “You just always kind of assume he’s going to be there. I got a 9-year-old son and in the back of mind it’s always been like, ‘Oh, it would be great for him to play for coach Parker.’ Obviously, that’s a long time away. You just kind of always think of him being here running the program. It will definitely be a change.”

Parker is leaving the bench, but not BU. He’s going to work as a fund-raising special adviser to Brown, and has a contract that goes through 2017-18.

The obvious question about Parker’s retirement is whether this is his choice or someone else’s? Is he walking away or being nudged out after the school dealt with two embarrassing episodes of alleged sexual misconduct by hockey players in a 10-week span last season, causing the university to do some serious soul-searching and an internal investigation.

Lynch was asked if Parker would be the coach next season if he had not decided to retire. “Oh, yeah, this was his decision,” he said.

The task force BU established a year ago released its findings in September. The ice hockey inquisition declared that the team’s “elevated social status” fostered a “culture of sexual entitlement” among some players. The top recommendation of the task force was to strip Parker of his title as executive director of athletics.

“People have asked whether this will tarnish my legacy here or will this be a bad thing for the university in the long run,” said Parker. “The only way I can put it for you is that people have their opinions of what went on. Everybody is welcome to their opinions. The people that I’m most concerned about know what BU hockey is all about . . . We’ve incorporated the stuff that the task force has asked us to do. We were doing a lot of it already. I think our program is better for it. I know our program is better for it. I’m proud of the way my team handled it.”

It’s been a trying 40th season for Parker.

Two players left the team in the midst of the season, unhappy with their playing time. BU lost in the first round of the Beanpot to Northeastern during a slump in which the team went 3-8-2.

Freshman goalie Matt O’Connor was lost for the season earlier this month to a collapsed lung. The Terriers lost defenseman Garrett Noonan to a separated shoulder on Friday in a 4-2 win over Northeastern.

“You don’t really coach for the outcome. You coach for the process,” said Parker.

Only his players can delay Parker’s retirement a little longer.

BU (18-15-2) is the third seed in the Hockey East tournament, facing off with Merrimack in the first game of a best-of-three series on Friday.

There were dalliances with Yale early in his career and Causeway Street later on. But Parker’s heart — like all of his victories as a coach — remained at BU until the end.

“It’s been a great ride, and I’ll remember it all,” said Parker.

Parker should be remembered as more than a hockey coach for BU, as a champion of the university.