Navy Coach George Welsh, calling it an agonizing decision, told his football players tonight that he has accepted the job of coaching at the University of Virginia.

The formal announcement will be made at an 11 a.m. Wednesday news conference in Charlottesville.

"I told the squad that there's a time to stay and a time to leave and, for me, I feel it's time to leave," Welsh said tonight. "The meeting lasted 15 minutes and I did all of the talking. There weren't any questions. Besides, what could they say? I'm going to see them all again Thursday anyway."

Welsh will coach Navy against Ohio State in the Liberty Bowl in Memphis Dec. 30. Practices for that game will begin Thursday.

The Midshipmen have been in final exams this week and have not played since Army tied them, 3-3, on Dec. 5.

In his nine years here, Welsh's teams had a 55-45-1 record.

At Virginia, Welsh will replace Dick Bestwick, fired last month after compiling a 16-49-1 record in six seasons. The Cavaliers were 1-10 last season. In 1979, Bestwick's team had a 6-5 mark for Virginia's second winning season in 29 years.

On numerous occasions in the past, Welsh has been approached by other colleges interested in offering him jobs, some of them more attractive than the one he has accepted. There was speculation that he might succeed Joe Paterno at Penn State, but Paterno has no plans to give up coaching.

Welsh said he had agreed to a multiyear contract at Virginia, but chose not to discuss the terms of it. The Virginia contract is believed to be worth about $100,000 a year; Welsh is estimated to have earned $60,000 at Navy.

"This wasn't a financial decision," he said. "And I'm not getting the big bucks I read they are offering (Jerry) Claiborne at Kentucky. The compensation is good, but I'm not going for more money.

"This was a very difficult decision to make. I'm 48 and I first came to Navy when I was 17, so I've spent about half of my life here as a student, an assistant coach and as head coach. It's tough to break the ties sometimes, but I feel this is the right thing for me to do. I feel we are parting on good terms.

"I've had a great relationship with the athletic director (C.O. Coppedge), and I'll always be grateful to him for making me a head coach."

Welsh said the move had happened so suddenly that it has left him both emotionally and physically drained. He said that when Virginia first contacted him a week ago, "I had no idea it would lead to this. They said they wanted to talk to me and I said I'd listen."

Welsh said he went to Charlottesville to talk to Dick Schultz, Virginia athletic director, Friday. "I spent Saturday and Sunday contemplating what to do. I called down there Sunday and we made a tentative agreement, and I called back again Monday and accepted the offer.

"With this being finals week, there just wasn't enough time to get the squad together until today, so that's why it got dragged out so."

Welsh met with Coppedge Friday and with the eight-member Naval Academy Athletic Board Saturday and they tried in vain to get him to stay.

Welsh said last night that it was difficult to explain why he is leaving, but it wasn't because he was unhappy at Navy.

"I told the players at the meeting that I thought they were a great bunch of young people with love and respect for each other and that is a reason for their success," he said.

Coppedge, who wasn't available for comment tonight, said earlier this season that Welsh was the reason Navy football had improved dramatically, and, if he left, it would be extremely difficult to replace him.

"I don't want to put any pressure on the new coach," Welsh said, "but I think the talent is here. I'd like to see the program continue to win seven or eight games a year, but with the teams Navy plays in the future it will be tough to win any more than that."

There were no names being mentioned here tonight as a possible successor. Roger Staubach, the former Navy quarterback who went on to stardom with the Dallas Cowboys, said yesterday from his Dallas office that he had no interest in coaching.

The Liberty Bowl will be the last game as Navy coach for Welsh, who quarterbacked Navy to an upset of Mississippi in the 1955 Sugar Bowl. Ironically, the first team he will face next season at Virginia will be Navy, and the game will be played in Annapolis.