Sotheby's is going, going . . . gone to the highest (American) bidder

The fate of the London-based fine art auction house, Sotheby Parke Bernet, has finally been decided, after months of uncertainty and bitter public wrangles that have held the financial world spellbound.

The venerable British institution is to be turned over, for the handsome price of (STR)83 million ($124 million), to an American, millionaire businessman and art collector Alfred Taubman - reputed to be one of the richest men in the United States. He plans to take the company back into private ownership.

Mr. Taubman's takeover has the blessing of the British government and of Sotheby's managers, who have been promised they will be allowed to retain their jobs. The US businessman's offer of (STR)7 ($10.70) a share has been given the green light by the Monopolies and Mergers Commission. After investigating Mr. Taubman's credentials, the commission said it saw no reason to block the sale.

The future of Sotheby's - which posted a $4.5 million pretax loss in 1982 - had hung in the balance since May. At that time the commission was called in to investigate an earlier bid by two other Americans, Marshall Cogan and Stephen Swid, who head General Felt Industries, the world's largest manufacturer of carpet underlay.

The Cogan-Swid bid was fiercely opposed both by Sotheby's board and by its unique staff of art experts, who felt that the Americans were ''totally unsuited'' to the task of running this highly specialized business. Sotheby's art experts threatened to resign ''en masse'' if Cogan and Swid succeeded.

Pressure from Sotheby's directors persuaded the government to order a monopolies commmission investigation into the proposed purchase. Soon after, Mr. Taubman emerged as a potential bidder - the ''white knight'' Sotheby's had been seeking to rescue the company and ward off the unwelcome Cogan-Swid offer. Mr. Taubman's bid, too, automatically went under the commission's microscope.

Sotheby's looked on Mr. Taubman, whose business acumen is legendary, much more kindly. In the words of the company's chief executive, Graham Llewellyn, this time around ''the chemistry was right.''

What is more, Mr. Taubman, who said his bid was ''like coming over (to Britain) and buying the throne,'' has impeccable connections in the art world. A collector for 30 years, with a particular interest in Impressionist paintings, Chinese ceramics, and 20th-century art, he is a trustee of the Michigan Foundation and sits on the board of New York City's Whitney Museum of American Art.

Mr. Cogan and Mr. Swid have conceded defeat: They are selling their 29.9 percent stake in Sotheby's to Mr. Taubman, which, by way of consolation prize, will bring them a quick $10.7 million profit.

Mr. Taubman, who owns more than 12 percent of Sotheby's, is scheduled to visit London today to announce his bid formally.

British art experts feel that under American control, the focus of Sotheby's activities will slip more and more toward New York. But Mr. Taubman has stressed that the headquarters of this quintessentially British institution will remain in London, and that the British end of the business will continue to be run from Bond Street, in the heart of town.

The size of Mr. Taubman's offer has taken the city by surprise. Although Sotheby's expects profits for this year to surpass $6 million, many consider that $10.70 a share is grossly overvalued.

Many believe that if Mr. Taubman is to make a success of restoring Sotheby's fortunes, the traditional accent of the business may have to shift away from fine art. One area that Mr. Taubman will likely be keen to develop is Sotheby Parke Bernet Realty, an already flourishing subsidiary.