Mr. Prendergast, 64, has spent more than 25 years at the authority. His term at the helm brought stability to an agency that had had three leaders in the four years before his ascent.

His current term is set to expire in 2021, although few recent leaders have served more than a few years in the demanding job. Mr. Cuomo said Mr. Prendergast was leaving to deal with personal matters.

Mr. Prendergast, who grew up in Chicago, often seemed more comfortable with the technical aspects of running the authority’s vast network of subways, buses and commuter railroads than with the difficult political questions he often encountered. His top priority had been persuading state and city leaders to fund the agency’s roughly $29 billion capital spending plan to pay for the system’s maintenance and expansion. The plan was approved last year after months of heated debate between Governor Cuomo and Mayor Bill de Blasio.

As president of New York City Transit, leading the city’s subways and buses, Mr. Prendergast was praised for overseeing the system’s swift recovery after Hurricane Sandy in 2012. He became the Metropolitan Transportation Authority’s chairman after Joseph J. Lhota, a Republican, resigned to run for mayor, losing to Mr. de Blasio, a Democrat.

Despite Mr. Prendergast’s transportation experience, some have criticized his acquiescence to Mr. Cuomo, who appointed him to the job and has effectively controlled the authority. Mr. Prendergast oversaw the agency at a time when many subway and bus riders said service was getting worse and were frustrated by regular fare increases.

Mr. Cuomo said he had a few weeks to find a replacement for Mr. Prendergast. He declined to discuss possible candidates, but he said the successful candidate must have experience operating a transit agency as well as deep experience as a developer “because a lot of what the M.T.A. does is also build.”

“We’re building on the Long Island Rail Road, Penn Station, Farley Station, so it’s a difficult mix of talents,” Mr. Cuomo said.