The Rockefeller Group, the owner of Rockefeller Center, Radio City Music Hall and other mid-Manhattan office buildings, said yesterday that it had sold control of the company to the Mitsubishi Estate Company of Tokyo, one of the world’s biggest real estate developers.

Richard A. Voell, Rockefeller’s president and chief executive, said Mitsubishi would pay $ 846 million in cash for a 51 percent interest. The proceeds will go into the family trusts established by John D. Rockefeller Jr. in 1934 and be used to diversify the family’s holdings.

The deal, which comes almost exactly 50 years after Rockefeller Center opened on Nov. 1, 1939, is only the latest instance of the Japanese buying a vital piece of the American landscape, from Hollywood to Wall Street. In September, the Sony Corporation bought Columbia Pictures for $ 3.4 billion.

David Rockefeller, the company’s chairman, said in a statement that the agreement ”preserves the abiding commitment to Rockefeller Center and New York City which my father made more than 50 years ago, and which present generations of the family continue to feel.” There has been talk that the 88 Rockefeller descendants, all beneficiaries of the 1934 trusts, had wanted to take advantage of high Manhattan property values and turn their stakes into cash. ‘Nobody’s Cashing Out’

Asked in a telephone interview yesterday afternoon whether the Rockefeller Group was selling because some of the family might want cash, Mr. Rockefeller replied, ”Nobody’s cashing out.”

The sale to the Japanese came as no surprise in real estate circles. People close to the deal said in mid-September that to give the Rockefellers more ready cash, the family was trying to raise as much as $ 1 billion.

Jotaro Takagi, president of Mitsubishi Estate, said: ”There is no business address in the world that has the same cachet as Rockefeller Center. It is synonymous with excellence. We are making this investment with the objective of continuing this tradition into the 21st century, sharing with the Rockefeller family the vision of the center as a very special place in New York City, and of the city itself as a world capital of business and culture.”

Since the 1930’s, Columbia University had owned the land under the original Rockefeller Center running down the east side of the Avenue of Americas to Fifth Avenue and from 48th Street to 51st Street. But the Rockefeller Group bought it in 1985 for $ 400 million.

Mr. Rockefeller, who is 74 years old, is one of two surviving children of John D. Rockefeller Jr., who had five sons and one daughter. The other is Laurance S. Rockefeller, 79, owner of the Woodstock Inn in Woodstock, Vt., and former chairman of Rock Resorts.

Mitsubishi, a name closely linked to everything from banking and trading to shipbuilding and automobiles, joins three other business leaders that already have a big stake in the Rockefeller properties. Owners of About 6.5 Percent

The Agnelli family of Italy, headed by Giovanni Agnelli, chairman of the Fiat automotive group; Belton Kleberg Johnson of the family that owns the enormous King Ranch in Texas, and Patricia and William Hewitt of Moline, Ill., own a total of about 6.5 percent of the company. Mr. Hewitt is a former chairman of Deere & Company, the farm machinery manufacturer.

Mr. Voell said in September that the Rockefeller company was exploring several possibilities, including a sale or a joint venture with what he called ”selected investors who share the long-term interests of the Rockefeller Group.”

The search, begun in the summer, had been expected to take far longer, but even then had been centered on Japan and other Asian points. When Mitsubishi Estate was approached in the late summer, it agreed almost immediately to make a pre-emptive bid, ending any further discussions with other Japanese companies.

Initially, the Rockefeller company said, Mitsubishi would own some 627,000 shares, or 51 percent, but in a sign that both sides expect the percentage to rise, the formal announcement said the Rockefellers would be able to transfer more stock to Mitsubishi or to others acceptable to both parties.

In Japan this morning, people close to the deal said Mitsubishi would increase its stake to 80 percent in two to three years. Decision by Family Trust

David Rockefeller stressed in the interview, however, that the Rockefeller family would have no control over the decision, which would be made by the family trusts. The trusts are controlled by an independent committee headed by William G. Bowen.

He explained that the trust committee invested funds for the six Rockefeller children and their descendants and that the Rockefeller Group investment ”had done extremely well and had grown significantly faster than other assets in the trust.”

Mr. Rockefeller maintained that it was now ”a matter of prudent management to diversify” into other areas. ”The proceeds of the sale will be used to purchase other investments,” he said.

Dr. Bowen, a former president of Princeton University and now president of the Mellon Foundation, stressed that ”none of the proceeds go to the beneficiaries,” meaning the Rockefellers. ”They remain in the trust,” he said. Largest Single Investment