The Justice Department ended 3 1/2 years of litigation against Fairfax County yesterday by accepting the county's offer to distribute $2.75 million in back pay to 685 alleged victims of race and sex discrimination.

Justice officials said the settlement is the largest back pay award they have ever won from a state or local government and proves the Reagan administration's commitment to equal opportunity.

The county agreed to pay an average of $4,000--and in two cases more than $32,000--to blacks and women who were denied jobs or promotions during the past 10 years. Fairfax also agreed to hire 150 of the alleged victims within the next two years as jobs become available and to pay about $170,000 in social security taxes in addition to the multimillion-dollar settlement, which was signed by Alexandria U.S. District Judge Albert V. Bryan Jr.

"Obviously, this proves that Fairfax County was not fulfilling its commitment to affirmative action," said County Board Vice Chairman Martha V. Pennino. "This is a fine against all the people of Fairfax. . . We all share the guilt."

Pennino's view contrasted sharply with the official position of the county, which spent more than $1 million contesting the lawsuit and admitted no wrongdoing in the consent decree. Fairfax Board Chairman John F. Herrity, a Republican, last year lobbied President Reagan and Attorney General William French Smith to drop the suit, brought during the Carter administration, on the basis of Reagan's campaign pledge to stop harassing local officials.

But the federal government, which had lost the case in 1979 only to win a new trial on appeal, decided to press the suit. Last April, Bryan said the government had established a "pattern and practice of disparate treatment of blacks" in professional, technical and public safety jobs, and of women in paraprofessional and maintenance positions.

More than 1,900 people applied for damages and though the county reserved its right to appeal, the court appointed a special master to hear their claims one at a time.

The consent decree, which the county's nine elected supervisors tentatively approved in January, will end the need for those hearings, which might have led to a county liability of more than $15 million, according to the estimates of county attorneys. The settlement also allows the county to maintain its innocence and to escape any court-imposed quotas in hiring.

"We have won on several issues and we have lost on several issues," Herrity said yesterday through a spokesman. "The federal government is camped on the opposite shore of the Potomac with the legal troops to make the cost of further litigation more expensive than settlement."

William Bradford Reynolds, assistant attorney general for civil rights, said the settlement proved the administration's determination to demand fairness in hiring without imposing quotas. "It underscores once again the administration's commitment to enforcement of the civil rights laws on behalf of all individuals who have been injured by discriminatory conduct, no matter how large the group of victims," he said.

A Justice spokesman said the largest back pay award until yesterday was a recent $975,000 settlement in a case involving police in Nassau County, N. Y. Expecting the settlement, the Fairfax Board this week set aside enough money to pay the award from the 1983 budget.

The individual awards were based on how much a claimant would have earned since the alleged discrimination occurred. Jesse Sutphin, who retired from the county inspections department in January, will receive $32,731.75 before taxes because she was denied promotions beginning in 1972, allegedly because of sex discrimination, county officials said. Sutphin was unavailable for comment yesterday.

A current employe, Christopher Stokes of the juvenile court, was also awarded more than $32,000 because of past denials of promotions, allegedly because of race discrimination. Stokes was home sick yesterday and said he did not want to talk about the award.

The 1980 census found 596,901 people in Fairfax, 5.9 percent of them black and 14.6 percent classified as minority. When Justice filed its suit in 1978, it said the county work force was 5.6 percent black. County officials said more than 11 percent of their 5,800 full-time workers today are black.

"I think things had changed before they brought the suit," said county attorney David T. Stitt. "The affirmative-action plan was in place before we ever heard of these people at Justice ."

The consent decree accepts the county affirmative-action plan, but orders the county to report on its hiring progress every six months until 1987. It also places the county under permanent court injunction against discrimination in hiring.