Bobby Beathard, one of the most coveted general managers in the National Football League, signed a two-year extension of his contract yesterday committing him to stay with the Washington Redskins through the 1988 season.

Beathard's signature was a stroke of stability for the Redskins organization. Beathard, 49, who had one year remaining on his contract and had been courted by other NFL teams, said in a statement that he wants "to remain here until the end" of his football career.

"What I'm most happy about is that the hierarchy of our club is solidly intact," owner Jack Kent Cooke said yesterday. Coach Joe Gibbs is under contract through 1989.

Terms of Beathard's agreement, which was reported last month in The Washington Post, were not disclosed. The deal was completed about six weeks ago, but Cooke and Beathard had commitments that delayed the signing until yesterday.

Beathard, the Redskins' general manager since 1978, received queries from the Dallas Cowboys and the San Diego Chargers.

He has declined to comment on those situations and was not available for comment yesterday.

After the Cowboys reorganized their front office, President Tex Schramm said last month that he called Beathard to check on his status with the Redskins. Schramm said he told Beathard he had heard what had become persistent, league-wide rumors that Beathard might become the Chargers' general manager in 1987.

Schramm quoted Beathard as saying, "No, I'm very happy where I am."

At the league's owners meetings last month, Chargers owner Alex Spanos said he and Beathard had talked but did not discuss a job for Beathard.

Rumors about a move to California have followed Beathard for about a decade, from his days as player personnel director of the Miami Dolphins. Beathard is from California, his parents still live there and he has invested in a condominium north of San Diego, where he eventually hopes to settle.

Yesterday, in a statement released by the team, Beathard silenced the rumors.

"This is the best football city in the United States, and, needless to say, I also think this club is the best organization in the NFL."

The Redskins have reached an agreement with free agent kicker Steve Willis. Willis, from Kansas State, and former Maryland kicker Jess Atkinson will compete with several others in a tryout Monday at Redskin Park.