The Federal Home Loan Bank Board, in an action that could trigger a fundamental change in the structure of the nation's banking system, yesterday approved the acquisition of Fidelity Savings and Loan of San Francisco by Citicorp, the country's second-largest bank holding company.

This marks the first time that a bank in one state has been allowed to take over an S&L in another. If also approved by the Federal Reserve Board, the acquisition could pave the way for a national banking system, bypassing a prohibition against branching across state lines without the permission of the host state. It also would put Citicorp into direct competition with Bank of America, the nation's largest bank.

Bank of America denounced the action as "piecemeal deregulation." William B. O'Connell, president of the U.S. League of Savings Associations, called it "a major blow against the important American tradition of keeping financial power diversified and decentralized."

California's Savings and Loan commissioner, Linda Tsao Yang, who bitterly fought the decision, termed it a "tragedy" and a "prime example of the arrogance of regulatory powers to defy the spirit of laws made by Congress." Legislation setting the priority for mergers of like institutions within the same state first and dissimilar institutions across state lines last is stalled in the Senate.

Under the terms of the acquisition, Citicorp, with assets of $120 billion, would pump in more than $80 million to shore up Fidelity's net worth. At the same time, the Federal Savings and Loan Insurance Corp. would provide an estimated $165 million in aid over a 12-year period. Citicorp has agreed to repay some of that assistance under a complicated formula.

Federal regulators seized the $2.9-billion-asset S&L last April because they feared it would become insolvent, an action a federal judge later ruled illegal. Bids were solicited from institutions interested in taking over Fidelity. The bank board said Citicorp's bid was $143 million better than that of the nearest competitor. The other bidders were Californians.

Citicorp, the parent company of Citibank, has 853 offices in 40 states and the District of Columbia. In California Citicorp has 38 offices for commercial lending, leasing and research operations. Fidelity has 81 branches in the northern part of the state.

BankAmerica Corp., with $121.5 billion in assets, has 1,094 branches in California and international banking operations in 10 states and Nassau. Should Citicorp acquire Fidelity, it would become the largest bank holding company in the country.