NEW YORK (AP) _ One of Wall Street's largest securities firms and its London-based sister company have announced their agreement to merge, following more than six months of negotiations.

First Boston Corp., which is based in New York, and Financiere Credit Suisse-First Boston had grown increasingly competitive, one motivation behind the merger talks.

In announcing the agreement, approved by First Boston's board after five hours of meetings Sunday, the two firms said: ''The new structure will help the two organizations overcome strains that have developed in their relationship because of the far-reaching changes in the global marketplace.''

The Swiss banking conglomerate Credit Suisse will own 44.5 percent of the combined new entity, giving it effective control and the largest foreign stake in a major Wall Street securities house.

Credit Suisse will also become the only commercial banking concern to control a major securities house. Banks are prohibited in the United States from holding such large stakes in securities firms, as a provision to separate commercial banking and securities underwriting activities.

Credit Suisse, among Europe's largest banking companies with almost $68 billion in assets at the end of last year, is able to take the stake because it held its interest before the law against such holdings took effect. Staff at the Federal Reserve approved the arrangement last week, The New York Times reported today.

The combined entity, which will be privately held, is to be called CS First Boston Inc. and headquartered here. The complex merger will involve buying out First Boston's existing public shareholders at $52.50 a share in cash, a total buyout cost of $1.1 billion.

The merger of the two firms, both among the world's largest providers of financial services, is part of a trend toward partial foreign ownership of top U.S. investment houses and could offer a model for Wall Street on the road to a global financial system, the Times said.

Peter T. Buchanan, First Boston's chief executive, said the firm is negotiating to bring in other foreign investors to purchase 30.5 percent of the new entity.

Buchanan indicated that the additional investors would be from Japan or elsewhere in the Pacific Basin to give the firm better contacts in that market.

Until other investors are found, the 30.5 percent stake will be bought and held by a friendly investor, First Boston said. In an unusual step, the firm refused to name the friendly investor. It said it would be identified before the merger is completed.

The merger will shake up senior management. Credit Suisse chairman Rainer Gut, 55, who has been outspoken in his displeasure with aspects of First Boston's performance, will become chairman of CS First Boston upon completion of the transaction.

Buchanan will become chief executive of CS First Boston but only until the fall of 1989, when he will retire at age 55, following through on an existing plan.

Buchanan will be succeeded next year by John M. Hennessey, a former First Boston official who has been chairman of Credit Suisse First Boston in London. The Wall Street Journal said Hennessey has the strong support of the Swiss, for whom he has effectively worked.

First Boston chairman Alvin Shoemaker, 49, whom Buchanan had previously described as his successor, will instead retire at the end of the year.

First Boston has suffered several setbacks in the last two years, including the departure in February of its two best deal-makers, Bruce Wasserstein and Joseph Perella. The men left to form their own investment bank.

Among other troubles, the firm had a loss of about $100 million in trading risky options on Treasury bonds in the summer of 1987 and had another $50 million loss in trading mortgage-backed securities. Its mortgage securities chief, its head of municipal finance, its head of risk arbitrage, seven members of its leveraged buy-out group and several others either left or were asked to leave, the Wall Street Journal said.