Hochul thanked Zucker for his service and said he has agreed to stay on until the state names a new commissioner.
Zucker, who was appointed by Cuomo as health commissioner in 2015, was a leading figure in the state's pandemic response last year as the New York City metro area became one of the world's worst COVID-19 hot spots.
Cuomo often praised Zucker for his leadership, and the two appeared together regularly at the Democrat's widely watched televised briefings.
Under Zucker, the department of health worked with hospitals statewide to ensure that a surge of COVID-19 patients wouldn’t catastrophically overwhelm hospital systems.
But Zucker has faced heated criticism over the state’s COVID-19 response, particularly in nursing homes.
Over 15,800 people living in nursing homes and other long-term care homes in New York have died of COVID-19, according to data released by the state this year.
Zucker has defended a since-rescinded March 2020 directive that said nursing homes couldn’t refuse to admit patients solely because they had COVID-19.
Zucker and Cuomo have said the directive was needed to ensure elderly patients weren’t languishing in hospitals.
Hochul said Thursday that she was following through with her previously announced intentions to hire her own team.
“I am looking to build a new team,” Hochul said.
Zucker has also faced criticism from health care workers who said the state failed to ensure hospitals and nursing homes had adequate personal protective gear and staffing during the peak of the pandemic.