FORT WORTH, Texas (AP) _ Van Cliburn, who dazzled Muscovites by winning the 1958 Tchaikovsky Competition, will perform at the White House for Soviet leader Mikhail Gorbachev in the pianist's first public performance in nearly a decade.

The performance will be at the Dec. 8 state dinner for Gorbachev given by President Reagan, Cliburn said from his home here.

Another musician, conductor-cellist Mstislav Rostropovich, who fled from the Soviet Union in the mid-1970s, also will attend but will not perform, a source who spoke on condtion of anonymity told The Associated Press.

The 53-year-old Cliburn has neither recorded nor performed in public since 1978.

Twenty years earlier, he became the first American to win the gold medal at the Tchaikovsky piano competition in Moscow. That was just six months after the Soviet Union launched Sputnik, the first spacecraft.

On his return to the United States, he was given a hero's welcome, including a ticker tape parade in New York City and an invitation from President Dwight Eisenhower to perform at the White House.

In recent years, Cliburn has told friends of his desire to play before an audience again. The question narrowed to where and when. Whether this appearance will lead to a full-time return to his career is uncertain.

''Let's wait and see how it goes,'' Cliburn said. ''All I can tell you now is that I'm ready and will do my best.''

Cliburn is expected to play about 30 minutes for the Reagans and their guests after the state dinner. In recent months, he has been preparing music by Chopin, Brahms, Rachmaninoff and Debussy, and his choices for Washington will be drawn from this repertory.

Since spring, he has made his home in Fort Worth with his mother, Rhildia Bee O'Bryan Cliburn, who was his first teacher.