Ending a decade of debate about how to house Fairfax County's sprawling bureaucracy, the Board of Supervisors voted 8 to 1 last night to accept a novel land deal under which a developer will build an $83.4 million government center in a booming area west of Fairfax City.

The huge complex will provide offices for hundreds of Fairfax employes who overflowed the 12-story Massey Building -- the current county center -- years ago, forcing the county to spend more than $5 million a year for leased office space.

The board's decision also is certain to hasten development near the government center site at I-66 and Rte. 50, already the location of some of the Washington area's most opulent new construction.

The five-story center is planned for nearly 1 million square feet of office space, and could be the site of a large county cultural center. Construction on the first phase of the government center, which does not include the cultural center, could begin next year.

In return for the new headquarters, the county board agreed to give the developer $41.2 million in cash and other compensation and permission to build a huge mixed-use project of high-rise office buildings, hotels, town houses and garden apartments on 116 acres of land nearby.

"Yee-hoo!" whooped board Vice Chairman Martha V. Pennino (D-Centreville), the driving force behind the government center since it was proposed by a county commission in 1978, and one of the few board members who did not perform a flip-flop to vote for it yesterday.

"What will be created will be something of pride not only for the people of today but for those who come after in Fairfax County," she said.

The sole dissenting vote was cast by Supervisor Audrey Moore (D-Annandale), who agreed with the county's largest civic organization that the agreement was a giveaway by the county of enormously valuable land and a sweetheart deal for the partners in the development, the Charles E. Smith Cos. and the Artery Organization.

"I don't think you get something for nothing," she said.

Moore, as did the Fairfax County Federation of Citizens Associations, urged that the county borrow money through bonding to pay for the government center, a proposal most board members find politically unpalatable. She argued that the county would fare better financially by holding on to its land, which it bought in 1979 for $4.1 million and is worth $42 million today.

While the other eight board members generally acknowledged that the deal with Smith/Artery might be lacking, they argued strongly that it was not the county's business to speculate on land values. The agreement, they said, was the best way to build the acutely needed new county headquarters.

Further, Moore's proposal to finance the center through bonds was derided by board members who said they would rather use the county's finite bonding authority to pay for improvements to the county's roads, schools and parks.

Moore is the Democratic candidate for chairman of the county board against John F. Herrity, the Republican incumbent. There also are two independents in the race, James S. Morris Jr. and Robert T. Robarge. The election is Nov. 3.

In a written statement he distributed at the meeting yesterday, Herrity hailed the agreement with Smith/Artery as an example of "privatizing" the development of needed facilities "with little impact on the taxpayer . . . . "

He asked: "Why should Fairfax County use bonds to build a government center when bond financing is needed for far more critical priorities in the county such as transportation, schools, libraries and parks."

Herrity also cited an article in the magazine Development Trends 1987, a publication of the Urban Land Institute, which pointed to agreements such as the one between the county and Smith/Artery as the possible "wave of the future."

The article also raised complex questions about the relationship between developers and municipalities that enter into such arrangements, and asked whether a local government could remain an objective judge of a deal in which it is a partner. The article noted that local governments may give too much away to developers in their desire to strike a deal.

Herrity, a longtime opponent of the center, whose proponents he once accused of having an "edifice complex," helped breathe new life into the project two years ago when he endorsed the concept of a public-private partnership such as the one approved yesterday.

Officials of the Federation of Citizens Associations, who have questioned the legality and the prudence of the agreement, said yesterday they were considering asking Virginia Attorney General Mary Sue Terry for an opinion on the matter.

Even if Terry rendered an opinion favorable to the group, however, it would not block the project and would carry no precedential weight in court.

The saga of the proposed new government center parallels Fairfax's breathtaking growth since the Massey Building was constructed at a cost of $7 million and opened in 1969. Then, the county had 2,300 full-time employes and a population of about 450,000. Today, there are 8,700 full-time county workers and the population hovers around 700,000.

County planners say that if all goes as planned and the county's seat of government moves five miles to the west, the Massey Building could become Fairfax's public safety center, housing the fire and police departments.