Lorin Maazel, music director of the Cleveland Orchestra, has been named manager and artistic director of the world-famous Vienna State Opera. He will be the first American ever to hold the prestigious post and only the second non-Austrian to occupy the position.

Richard Strauss, the great German composer-conductor, was the director from 1920 to 1924. Among the other celebrated figures to hold the directorship have been Gustav Mahler, Bruno Walter, Felix Weingartner and Herbert von Karajan.

The historic announcement was made yesterday morning in Vienna, where Maazel, 49, is currently on tour with the Cleveland Orchestra, and here in Washington, where Austrian Ambassador Karl Herbert Schober made official what had been widely rumored in recent days.

Yesterday in Vienna, Maazel said, "I am keen that this house again be led in the fashion of Mahler and strauss. I have the full responsibility for the opera . . . I'll do whatever needs to be done without fear of stepping on toes."

Maazel's appointment will take effect on Sept. 1, 1982, after the retirement of the present director, Egaon Seefehlner. In a statement to the staff of the Vienna company, Maazel said yesterday that "I do not intend to be an absentee director," adding that he will move with his family to the Austrian capital and make his home there. Maazel and his wife, pianist Israela Margalit, have two young children.

Maazel was born in Paris, the son of American parents who discovered his musical talents at an early age. Following studies on the violin from the age of 5, he began to conduct as a 9-year-old prodigy at the Interlochen Music Camp. A few years later Arturo Toscanini invited him to conduct the NBC Symphony.

By the time he was in his 30s, Maazel had conducted most of the major orchestras in Europe.

In 1972, after the death of George Szell, Maazel was named music director of the Cleveland Orchestra, a position he has held since that time.

Under the terms of Maazel's contract, he will be in residence with the Vienna Opera eight months of the year. The other four months he will be free to accept outside engagements.