The fourth annual Kennedy Center Honors for achievement in the performing arts will be awarded to band leader Count Basie, actor Cary Grant, actress Helen Hayes, choreographer Jerome Robbins and pianist Rudolf Serkin, the Kennedy Center announced yesterday.

The honorees are chosen by the trustees of the Kennedy Center from nominations submitted by mail from a 79-member artists committee which this year included such prominent artists as Van Cliburn, Jacques D'Amboise, Douglas Fairbanks Jr., Rex Harrison, Paul Newman and Meryl Streep. The only criterion is "superior artistic achievement as performer, composer, choreographer, playwright, director or conductor," according to the Kennedy Center.

"I think it's an excellent selection of people who have a lifetime of experience," said Roger Stevens, chairman of the Kennedy Center.

The recipients will be feted with a weekend of activities late this year. The trustees of the Kennedy Center will host a dinner and award the honors on Saturday, Dec. 5.The following day, President and Mrs. Reagan will host a reception at the White House prior to the Kennedy Center Honors gala performance in the Opera House, which will be taped by CBS-TV, for later broadcast. The evening will end with a supper dance in the Grand Foyer.

Asked how he felt about being an honoree, Jerome Robbins replied, "Honored," and chuckled.

Last year's honorees were Leonard Bernstein, James Cagney, Agnes De Mille, Lynn Fontanne and Leontyne Price. Count Basie played piano at the dance after last year's Honors Gala.

"Fortunately, we've got a lot of good pickings," said Roger Stevens of the pool from which to choose honorees, "at least for the next couple of years -- by life expectancy. . . There are a couple of people I'd like to get, but they think they're too old."

Cary Grant, 77, who acted in movies for more than 30 years, is known for his wit and warmth in such films as "The Philadelphia Story," "Holiday" and "Bringing Up Baby." He was also seen in the Hitchcock thrillers "North By Northwest" and "To Catch a Thief."

"I don't think he's ever participated in something like this before," said George Stevens, a friend of Grant's. "He's shied away from it."

Helen Hayes, 80, began her stage career at the age of 5 and has come to be known as "The First Lady of the American Theater." She received a best actress Academy Award for "The Sin of Madline Claudet," and a best supporting actress Academy Award for "Airport."

Choreographer Jerome Robbins, 62, began as a dancer and performed in Broadway musicals. He is the choreographer of the Broadway musicials "On the Town," "Fiddler on the Roof" and "West Side Story." "It was the first time dance ever advanced the story line," said Roger Stevens of "West Side Story."

Band leader Count Basie, 76, is a composer and pianist. His band came out of Kansas City in the '30s and produced such tunes as "One O'Clock Jump," "Swinging the Blues" and "Woodside." Frank Sinatra and Tony Bennett have sung with his band.

Pianist Rudolf Serkin, 78, was a child prodigy who began his serious concert career in 1920. The Czech-born pianist made his American debut in 1933 in a sonata recital at the Coolidge Festival here and was first heard in New York as a soloist with the New York Philharmonic under Toscanini in 1936.

The Honors Gala will be produced by George Stevens Jr., chairman of the American Film Institute, and Nick Vanoff, who have produced all the past Honors galas. "We're just starting to work on the gala," said Stevens, reached in Los Angeles. He said he did not know which entertainers would be part of the gala, but that it would include artists who have known the honorees or somehow been associated with them.