In what the company claims is the biggest real estate lease transaction in history, American Express Co. has agreed in principle to pay in excess of $2 billion rent over 35 years for a 51-story office tower under construction at the end of Manhattan.

As part of the deal, American Express would sell its current headquarters on lower Manhattan to the real estate firm of Olympia & York for $240 million.

Olympia & York is also the developer of the new building, the largest of six office buildings the Canadian firm is constructing on the 14-acre Battery Park landfill site along the Hudson River.

James D. Robinson III, chairman of American Express, said today that the company needed to move from the quarters it has occupied since 1976 because of its recent growth, particularly the acquisition of Shearson Loeb Rhoades Inc. Most of the varied American Express operations now spread around the city will be moved to the new building in 1984-1985, but the Shearson/American Express subsidiary will continue to occupy four floors in the World Trade Center.

The sale of its current building will give American Express a $180 million capital gain that "will be used to restructure our investment portfolio," Robinson said.

American Express is the second major tenant for Olympia & York's massive development of 6 million square feet of office, retail and recreational space. In November, City Investing Co. agreed to lease 700,000 square feet of space in one of the buildings, and with American Express taking 2.3 million square feet, it will mean that half of the project is leased.

At a press conference at American Express headquarters called to announce the deal, Olympia & York President Paul Reichman said that, with two major tenants, he now feels confident enough to name the Battery Park development The World Financial Center.

Olympia & York, a privately owned firm based in Toronto, arrived on the competitive New York real estate scene less than a decade ago. In 1976 and 1977 the firm acquired 12 million square feet of office space during one of the city's periodic real estate slumps. Since then the values of those properties in midtown Manhattan have soared. The firm has gone on to become the major office developer in the city. According to Olympia & York Executive Vice President Michael M. Dennis, once the Battery Park project is completed, the firm will control more office real estate than the current leader, Rockefeller Center