The old Tiffany building - which for three-quarters of a century has stood as a venerable testament to the graciousness and opulence of Victoria-Era Fifth Avenue - has been sold to the Rev. Sun Myung Moon's Unification Church as a headquarters for a month-old "futuristic" newspaper.

The church, which blends modern Christianity, Eastern religion and ardent anticommunism with Moon as the self-proclaimed messiah, paid $2.4 million for the ornate building, whose seventh-floor tea room as the motif for Truman Capote's famous short story, "Breakfast at Tiffany's."

The building once housed the world-renowned jewelry collection of Louis Comfort Tiffany, which attracted such denizens of American society and finance as Lillian Russell, J.P. Morgan, Sarah Bernhardt and Diamond Jim Brady.

More recently the building at 37th Street and Fifth Avenue, which Tiffany and Co. vacated in 1940 in favor of its present location at 57th Street and Fifth Avenue, has fallen on hard times. A succession of landlords divided its once-elegant showroom floors, and currently its street-level floor is rented by a fast-food hamburger chain.

The Unification Church yesterday said the seven-story building - which was designed by Stanford White and copied after the Palazzo Grimani on Venice's Grand Canal - will now contain "one of the most-advanced news processing systems available allowing most editing and typesetting to be done by computer."

The Unification Church's newspaper, the News World, began publishing Dec. 31 in the old 2,000-room New Yorker Hotel, which was purchased by Moon late last year for a reported $5 million.

The News World is a politically conservative morning newspaper which, its critics say, is attempting to proselytize its readers under the guise of being a standard news publication unaffiliated with any religious organization.

The paper, which places heavy emphasis on Asian affairs and devotes much of its space to anticommunist news and analysis, last month claimed a start-up distribution of 150,000 copies. However, its paid circulation is a puzzlement because a number of news dealers in Manhattan have said they routinely are given bundles of the paper without any request for payment.

Some advertisers have claimed their ads have been run without charge by the News World.

Michael C. Trulson, general manager of News World Communications Inc., which is owned by the Unification Church, said the newspaper's move into the Tiffany building will be completed this spring.

"We want to restore the building to some of its former elegance," said Trulson. He said there are tentative plans to restore the building's seventh floor tea room.

The business and news offices of the newspaper will be housed in the Tiffany building. The paper will continue to be printed in Mt. Kisco, N.Y.

Tiffany and Co. was founded in lower Manhattan in 1837. Its 37th Street Beaux Arts structure had been build in 1905 at a cost of $600,000 and included the well-known nine-foot Atlas statue holding the famous Tiffany clock.

The land, purchase then for a reported $2 million, marked the highest price ever paid for a Manhattan commercial site.

In those tax-free days, jewled garters priced at $2,000 apicee and $750,000 natural pearl necklaces were commonplace sales and Louis Tiffany's opalescent "Tiffany glass" became a favorite of the art nouveua movement.

During World War I Tiffany stopped making expensive baubles and turned to around-the-clock production of surgical instruments for the government. But in the 1920s the store reverted to luxury items and began producing the fashionable 1920s diamond "headache bands" for the Flappers of the time.

The building's purchase by the Unification Church marks another of a series fo major New York City real estate transactions by the Moon followers, and the deal seems certain to open another dispute with the city government over proposed tax-exempt status.

Besides the old New Yorker Hotel at Eighth Avenue and 34th Street, the Unification Church last year purchased the Manhattan Center next door for an estimated $1 million; the former Columbia University Club at 4 West 43d St. for $1.2 million, and a candy factory in Long Island for $700,000.

The church also owns several brownstone residences and midtown storefronts and has bought 350 acres in upstate Barrytown for $1.5 million.

Last month, the New York City tax commission conducted a hearing into the church's application for tax-exempt status, but it has made no ruling.

The hearing was marked by acrimony, with Unification Church president Neil Salonen angrily refusing to answer several questions by the commission and asking that reporters and photographers be barred from the hearing room.

When asked by the commission whether any of the seven trustee of the Freedom Leadership Foundation, an organization affiliated with the church, were members of the Moon sect, Salonen refused to answer, saying, "I don't consider it an appropirate question."

In convening the hearing, commission members said what was at issue was not the church's ideology, but whether, in fact, it is a religious organization and will use the property in furtherance of its religious purposes.

Marshall Kaplan, chairman of the commission, said yesterday that denying tax exemp status "is a very tricky procedure, because there's not much you can do when they're running a religious operation."

He said the Jehovah's Witnesses, among other groups, has tax-free status for publications and church-related operations. At the Jan. 5 hearing cirtics of Moon's sect charged that the Unification Church is a political organization based in South Korea and should not be considered a religion.

Kaplan said the tax-free status may be decided in several weeks.