In his speech, Mr. Cuomo thanked Mr. Schneiderman for his office’s efforts in negotiating the settlement with Entergy. The agreement involves the withdrawal of the state’s challenges and is expected to clear the way for Entergy to renew the licenses with the federal Nuclear Regulatory Commission.

Mr. Mohl said Entergy intended to shut one of the reactors by April 2020 and the other by April 2021. (A third reactor at Indian Point, the first to operate there, was shut down in 1974.) But he said the company planned to seek renewals of the licenses until 2024 and 2025 in case the operator of the state’s power grid determined that the plant must keep running longer to ensure reliability.

Mr. Mohl disputed any suggestion that Entergy had been pressured into agreeing to the shutdown, repeatedly asserting in an interview that the decision was made for economic reasons.

“We certainly respect the governor,” he said later at a news conference. “He’s entitled to say what he wants to say. We know what the facts are, and the facts are we made this decision based on the economics of the plant.”

Entergy, which is based in New Orleans, has been withdrawing from nuclear power generation in the North and focusing on its regulated utility business in the South. Mr. Mohl said the company would provide incentives to the workers at Indian Point to stay on through the shutdown. The company will offer displaced workers the chance to relocate to one of the company’s other facilities.

State officials said the impact on ratepayers would be negligible, adding that the governor’s office had estimated that, at most, the proposed shutdown would add $3 a month to electric bills in the New York City area. Utility customers in the city already pay rates that are higher than anywhere in the United States, except Hawaii.

James T. Slevin, the president of Local 1-2 of the Utility Workers Union of America, which represents about 350 workers at Indian Point, said: “Indian Point provides clean, affordable energy in abundance, which helps stabilize rates for ratepayers. New Yorkers are going to get hit hard in their pocketbooks when this shakes out.”