Eleven winners of the National Medal of Arts, which recognizes both artistic excellence and support of the arts, were announced yesterday in Venice by President Reagan.

Seven of them are artists: painter Romare Bearden, singer Ella Fitzgerald, poet Howard Nemerov, choreographer Alwin Nikolais, sculptor Isamu Noguchi, composer William Schuman and poet Robert Penn Warren.

The four honored for their patronage are Midwest opera supporter J.W. Fisher, oil magnate Armand Hammer and Richmond art collectors Sydney and Frances Lewis.

The winners, who are nominated by a special committee of the National Council on the Arts and forwarded to Reagan for approval, will be honored at a White House luncheon June 18.

This is the third year for the awards, which were proposed by Reagan in 1983 and approved by Congress in 1984. No more than 12 medals may be awarded per year to individuals or groups for their contributions to the "excellence, growth, support and availability of the arts in the United States."

Bearden, 72, a leading American painter, has had retrospective exhibitions at a number of museums, including the Museum of Modern Art and, in Washington, the National Collection of Fine Arts, now the National Museum of American Art. Raised in Harlem, Bearden has said that he wanted his work to bring the Afro-American experience into art and give it a universal dimension.

Fitzgerald, 69, a legendary jazz musician, is a pioneer in scat singing, a technique she developed during a tour with trumpeter Dizzy Gillespie in the 1940s. In 1979 she was one of the recipients of the annual Kennedy Center Honors, and in 1985 the National Endowment for the Arts gave her the American Jazz Masters Award.

Nemerov, 67, St. Louis poet and author of 23 books, is the recipient of every major American award for literature, including, in 1978, the National Book Award and the Pulitzer. Nemerov served as poetry consultant to the Library of Congress in 1963-64.

Nikolais, 76, was commissioned to create his first professional choreography in 1940. In 1984 the French government made him a chevalier in the Legion of Honor. He is a fellow of the Academy of Arts and Sciences and a member of the National Society of Literature and Arts and numerous other arts societies.

Noguchi, 82, was born in California but educated in Tokyo, and is known for blending the esthetics of East and West in a way that enriches both cultures. His work is in the collections of major museums worldwide. He established his own Isamu Noguchi Garden Museum in Long Island City, N.Y., in 1983.

Schuman, 76, has written 10 symphonies and five concertos, as well as overtures, chamber music and numerous other works for chorus, band and orchestra. He has served as president of the Juilliard School of Music and of the Lincoln Center. In 1943 he won the first Pulitzer Prize for music and was awarded another in 1985.

Warren, 82, was named the nation's first poet laureate in 1986. His work also includes critical studies, social commentary and 10 novels, the best known of which is "All the King's Men." Warren is the only person to have received two Pulitzer Prizes in poetry and one in fiction.

Fisher, 72, lives in Marshalltown, Iowa, and has been called a "Midwestern Medici." Since 1960 he has financed more than 60 new opera productions, including 17 full productions for the New York Metropolitan Opera and a number for the Washington Opera.

Hammer, 89, board chairman and CEO of Occidental Petroleum Corp., has given approximately $50 million to the arts since 1968. Among his donations are major contributions to the Los Angeles County Museum of Art, the Metropolitan Museum of Art, the Corcoran Gallery, the National Symphony and the Fogg Art Museum.

Sydney and Frances Lewis, 67 and 64 respectively, provided the money and a major collection of painting, sculpture and decorative arts that enabled the Virginia Museum of Fine Arts to build its new West Wing. The Lewises are known also for their collection of American craft and folk art