In a major victory for the national antiapartheid movement, the Board of Regents of the University of California, the largest university system in the country, agreed today to begin divestiture of $3.1 billion in South African-related investments.

The announcement of the 13-to-9 vote, piped through loudspeakers, sparked cheers and applause from antiapartheid students and faculty waiting outside the Santa Cruz, Calif., meeting room. With by far the largest block of South Africa-connected holdings of any American university, the decision by the nine-campus complex increased the amount of educational divestments by more than 450 percent.

"This answers the argument we are hearing that it is too difficult to divest large sums of money," said Joshua Nessen, national student coordinator for the American Committee on Africa. He said the California decision should inspire further efforts to force divestiture by large universities, such as Georgetown and Maryland, where demonstrators have called for selling all South Africa-connected holdings to pressure Pretoria to grant majority rule to blacks.

The California university vote, following a three-hour discussion, appeared strongly influenced by the decision of Gov. George Deukmejian to abandon his opposition to full divestiture. The regents agreed to give companies that had not recently increased their South African activities a one-year grace period to cut off ties to the minority white-ruled nation. University pension fund and endowment investments in companies that maintained South African ties after that would be sold within three years.

Deukmejian told the regents that their decision last year to divest only stock in companies that failed to meet certain civil rights standards in South Africa had given Pretoria a "strong, clear signal." To cheers from the crowd outside, Deukmejian concluded that "since conditions have changed in South Africa, it is appropriate to change our policies."

Deukmejian, a Republican who is seeking reelection, announced his change in position in a letter to the regents. It was made public two days before Los Angeles Mayor Tom Bradley, the Democratic gubernatorial nominee, was to appear before the regents. Bradley is a strong supporter of divestiture.

Some regents said they fear being sued if the divestment loses money for the university. Deukmejian promised to introduce legislation to protect them from such suits, and the regents voted to divest only if the legislation is enacted. Some regents argued that investments in a country in such turmoil is not good business practice.

According to antiapartheid movement organizations, 109 other schools have voted to divest $558 million. After California, the largest holder of South Africa-related investments is the University of Texas, with $700 million. A California official estimated divestment would cost about $118 million in commissions and other expenses.