General Electric Co. has agreed to buy RCA Corp. for $6.28 billion in cash, a historic merger of two of the world's best known companies that would create a global defense, communications and consumer products powerhouse with few, if any, equals.

GE's offer to pay $66.50 a share for RCA was approved by the boards of directors of both companies today. The deal is expected to be completed sometime next year after it has been approved by RCA stockholders and government regulators, including the Federal Communications Commission, the company announced in a joint statement just before 8 p.m.

Included among RCA's vast holdings is the NBC television network, currently the leader in prime-time ratings. GE's takeover of RCA means that in 1985, all three of the television networks -- ABC, CBS and NBC -- became targets of multimillion-dollar acquisition bids.

"We are creating a company that will successfully compete with anyone, anywhere in any market we serve," John F. Welch, chairman of GE, Thornton F. Bradshaw, chairman of RCA, and Robert R. Frederick, president of RCA, said in the joint statement.

They also said the merger is an "excellent strategic opportunity for both companies that will help improve America's competitiveness in world markets."

With $27.9 billion in sales last year, GE ranks ninth on the Fortune 500 list of the nation's largest industrial companies. It is about three times larger than RCA. The combined companies would have sales in excess of $38 billion and assets of more than $32 billion.

RCA stock shot up $10.75 today to $63.50 in anticipation of the announcement that was made about four hours after the market had closed. The stock had been climbing rapidly for the past several days, as rumors swirled through the market. Until tonight, RCA had steadfastly refused to comment or reply to questions.

The multibillion-dollar merger would combine two of the nation's premier high-tech companies, each of which is considered to be a major force in defense, consumer products, communications, and research.

The deal is a fitting climax to a year that has seen many of the best known corporations, including General Foods Corp., acquired by other giant companies.

In merger-mania's 1985 sweep through the broadcasting industry, RCA's television network becomes the third of the three major networks to become a takeover target. Earlier this year, American Broadcasting Cos. Inc. agreed to be acquired for $3.5 billion by Capital Cities Communications Inc., while CBS Inc. retained its independence by defeating a hostile takeover bid by Cable News Network founder Ted Turner.

GE and RCA each has a history linked to the growth and development of key sectors of American industry. For example, David Sarnoff, who was elected president of RCA in 1930 and remained active until his retirement in 1969, is recognized throughout the world as a pioneer in the development of radio, television and electronics.

With billions of dollars at its disposal, GE has been on the prowl for a major acquisition for the last few years. In RCA, GE will acquire a company that had sales of $10.1 billion and net income of $341 million last year.

In the first three quarters of 1985, RCA had sales of $6.4 billion and net income of $274.7 million. RCA had assets of $6.3 billion as of Sept. 30.

In addition to NBC, RCA owns television stations in Washington (WRC), New York, Los Angeles, Cleveland and Chicago. RCA also owns three AM and five FM radio stations in Washington, Boston, Chicago, New York and San Francisco. The acquisition of RCA would mark GE's return in a major way to the television broadcasting business, which it largely left a few years ago by selling all but one of the stations it owned.

RCA would also add to GE's considerable strength as a defense contractor. Among RCA's government contracts are the $307.6 million agreement to build the defense system for the Navy's 11th, 12th and 13th Aegis-Class guided missile cruisers. RCA designs, develops and produces a broad spectrum of military and space systems sold to the U.S. armed forces and to a lesser extent to foreign governments.

GE, which has a considerable communications network of its own, also would be gaining RCA's satellite communications systems. RCA's satellite systems provide voice and data transmission services worldwide.

RCA's prowess in consumer electronics, especially in televisions, would complement GE's focus on large consumer appliances such as dishwashers. There would be little overlap because GE has disposed of its own small-appliance and television manufacturing operations.

RCA also is a major force in the home entertainment and information industry. The company sells records, tapes, video cassettes and home video software to consumers.

RCA has long been rumored as a potential takeover target because the value of the company's assets exceeds RCA's stock-market value. A friendly merger with GE would guarantee that RCA management, rather than a hostile bidder, would determine who had control of the company's assets in the future.

In a statement to RCA employes, RCA's Bradshaw said:

"The decision to enter into such an agreement was not easy. Through all our efforts we have already successfully transformed RCA into a company with important market positions in electronics, communications and entertainment. With the strategic focus on our core business, RCA today is a powerful company with highly valued products and services.

"However, we recognize that it would take a bold and creative step to generate the critical mass essential to continued leadership in a global economy. By uniting our talents with those at General Electric -- a company with a similar commitment to technological and market leadership -- we will continue accelerating our momentum."

One of RCA's strongest ties to GE is through Frederick, RCA's president and chief executive officer. Frederick, who has been president of RCA for three years and who was elected chief executive officer in March, began his business career with GE in 1948.

Frederick spent his entire career at GE prior to joining RCA in 1982. In 1977, he was appointed senior vice president of corporate planning and development, a job he took after serving for four years as vice president in charge of its consumer products group. His last job at GE prior to joining RCA was as executive vice president in the firm's international sector.

Ironically, GE held a substantial interest in RCA from RCA's inception in 1919 until 1932 when GE sold its stake to settle a government antitrust suit.

The driving force behind the growth of RCA in its development as a dominant force in radio and television was Sarnoff, who died in 1971. In 1916, he proposed a "radio music box" that would receive programs broadcast for public information and entertainment. RCA's sales of home radios from 1922 through 1924 totaled $83 million.

As early as April 5, 1923, Sarnoff foresaw the possibility of television as a parallel service to radio. "I believe that television, which is the technical name for seeing as well as hearing by radio, will come to pass in due course," he told RCA's board of directors that year. The National Broadcasting Co. was organized by Sarnoff in 1926, when there were 5 million homes equipped with radio.

On April 30, 1939, Sarnoff launched his vision of television at the New York World's Fair with the statement: "Now we add sight to sound. This miracle of engineering skill, which one day will bring the world to the home, also brings a new American industry to serve man's material welfare. Television will become a factor in American economic life."

In 1944, the television broadcasters association conferred upon Sarnoff the title "Father of American Television." The first post-war television was introduced by RCA in 1946. By late 1958, RCA had produced its 10-millionth set.