In a telephone interview, Mr. Montebello said that after a packed fall season and the completion of several big long-term projects like new galleries for Greek and Roman art and European paintings, he felt the time was right.

“After three decades, to stay much further would be to skirt decency,” he said. "This has not been an easy decision — it’s wrenching for me, it’s been my entire life. But it’s time.”

James R. Houghton, chairman of the museum’s board, said he was not surprised by the announcement. “It has been in his mind for some time now,” he said in an interview. “It was a mutual decision and I think the right one.”

Yet he added: “To look for somebody to fill his shoes will be very hard. The pool of potential candidates is smaller than it once was.”