Levine, who turns 73 in June, suffers from Parkinson's disease, and his baton has become harder to follow this season.
Met general manager Peter Gelb said today that Levine will become music director emeritus and a successor as music director will be appointed "in the coming months."
While Levine intends to conduct in future seasons and will remain head of the company's young artists development program, the Met said his health has made it difficult for him to retain a full schedule.
Levine made his Met debut in 1971, became chief conductor in 1973 and music director in 1976. His title was upgraded to artistic director in 1986, a position he held until it reverted to music director in 2004, when he also became music director of the Boston Symphony Orchestra.
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He has led 2,551 performances of more than 85 operas with the Met, by far the most by an individual in the company's history. His tenure with a single orchestra is a rarity in a business where frequent podium shifts are commonplace.
"He has a unique ability to inspire those around him to perform to the best of their abilities and beyond."
The Met said it has a plan to appoint a new music director "who will be announced in the coming months." The favorites appear to be Yannick Nezet-Seguin, a 41-year-old Canadian who is music director of the Philadelphia Orchestra, and Giandrea Noseda, a 51-year Italian who is music director of the Teatro Regio in Turin.