“There was a dialogue I had with the governor going back a ways about how the work-life balance was starting to get out of kilter in my mind,” Mr. Prendergast said in an interview on Monday at his Lower Manhattan office. He agreed to stay through the opening of the Second Avenue subway this month, and he will oversee his last board meeting on Wednesday.

Gov. Andrew M. Cuomo, who has taken an increasingly hands-on approach at the authority, will choose Mr. Prendergast’s successor. Mr. Cuomo is considering several candidates for the job, according to a state official who has been briefed on the governor’s search but not authorized to discuss it publicly. The field includes Veronique Hakim, the president of New York City Transit, which operates the city’s subways and buses. If chosen, she would be the authority’s first chairwoman.

Ms. Hakim, 57, who is well liked, worked at the authority for two decades before becoming New Jersey Transit’s executive director in 2014. Mr. Prendergast praised Ms. Hakim, whom he hired for her current position about a year ago.

“She was the strongest candidate, and she was chosen for that job, so that tells you what my level of confidence is in her,” he said.

According to the state official, the governor is also considering Lawrence S. Schwartz, an authority board member and a former top aide to Mr. Cuomo, though Mr. Schwartz has said in the past that he was not interested in the job. The other candidates are Rick Cotton, an aide to the governor; Matthew Driscoll, the state transportation commissioner; Patrick Foye, executive director of the Port Authority of New York and New Jersey; Anthony Foxx, a former federal transportation secretary; Joseph J. Lhota, a former authority chairman; and John Porcari, a former federal transportation official.