Virginia Gov.-elect Gerald L. Baliles completed the announcement of his cabinet yesterday by naming Donald J. Finley, a budget specialist and career state employe, as secretary of education.

Finley, 46, who has been the education secretary since August, will oversee an issue that was a keystone of Baliles' election campaign and is likely to be plunged into the growing controversy over the level of state funding to local education in Virginia.

Before Gov. Charles Robb named him to the state's top education job, Finley was deputy secretary of finance and staff director of the influential House Appropriations Committee, assignments that will make him a critical player in the Baliles administration's effort to win more education money from the General Assembly.

At a news conference in Richmond announcing the appointment, Baliles praised Finley's "encyclopedic knowledge of the education budget." He said he had considered half a dozen candidates, but offered the $73,517-a-year job only to Finley, who holds a PhD degree in education from the College of William and Mary.

"During the campaign I often mentioned my commitment to education," Baliles told reporters. "I believe Dr. Finley's background will be invaluable in working to meet those commitments."

The first major issue facing Finley will be fulfilling Baliles' promise to work for full funding of the state Standards of Quality, the minimum standards for staffing, class size and other requirements for schools.

The state Department of Education estimated it would cost $419 million more in the 1986-88 budget than was appropriated in the last biennium. But a report earlier this month by the Joint Legislative Audit and Review Commission suggested that only $192 million more would be needed, drawing protests from local school officials who said the amount was too low.

Baliles and Finley, who will take office Jan. 11, declined yesterday to say how much they will seek in the 1986-88 budget, but both pledged to fulfill the campaign promise.

Northern Virginia school officials said they hope more state money will help even out an imbalance under which the state's more prosperous jurisdictions pay far more in state taxes than they get back in state revenue. Fairfax School Board Chairman Mary E. Collier said a major issue for Fairfax, the state's richest county, is whether the state "will recognize what it costs to provide quality education."

Finley said the joint legislative commission is to report in 1988 on the funding distribution issue, but major changes are unlikely, partly because of court decisions nationwide favoring state intervention to equalize spending between rich and poor communities.

"I'm not sure Northern Virginia should expect some major overall corrective action, although perhaps they might," he said in an interview. "I can empathize with their problem. No question -- they export more [money] than they import. But given the nature of school funding formulas and the whole court record behind it . . . that's sort of the name of the game."

Finley also faces the challenge of completing desegregation of Virginia's state college system. The Robb administration recently asked the federal government to relax its oversight of that process, saying much has been accomplished.

Finley said the state's higher education institutions were "a solid system that's on the brink of excellence." He said he would emphasize specific improvements such as increased links between economic development and education, citing as an example those between George Mason University and local high-technology businesses.

He said he already had discussed that idea with Richard M. Bagley, Baliles' commerce secretary-designate, and Finley's former boss as chairman of the House Appropriations Committee.

Finley will oversee the state college system, state aid to public schools, schools for the deaf and blind and other programs with an annual budget of $2.3 billion in state funds.

Finley said the Baliles administration was planning "a number of initiatives" in education, including increased business-education links and others he would not describe in detail. He said they will not require new spending, but "have more to do with planning, communication and thoughtful approaches to problems."

Finley's appointment drew praise from area legislators, including the probable future chairman of the House Appropriations Committee, Dorothy S. McDiarmid (D-Fairfax), who now heads the House Education Committee. McDiarmid, who recommended Finley to Baliles, said, "I don't know anybody who has a better mind.

"It would take anybody else at least two years to know what he knows," she said. "He knows the budget process in and out. He's hit the ground running."

Wayne F. Anderson, who was Robb's top finance official until last year and now is a teacher at George Mason, called Finley a "person of strength" who will need that quality in dealing with the state's independent-minded colleges and universities.

Anderson said states increasingly are recognizing the need to pair economic development with quality education in shoring up their economies, and that Bagley and Finley will be the "Damon and Pythias" to do that job for Virginia.

Finley holds bachelor's and master's degrees from the University of Richmond. He has been a state employe since he joined the state Council of Higher Education, where he worked until 1976.