The distribution network will be expanded to non-hospital providers, like CityMD, which will in turn expand the pool of eligible recipients.
Reservations will start Monday for both phases 1a and 1b, but health care workers in 1a must remain a priority, Cuomo said.
The expansion will cover police, correction officers, some essential workers, and people who are 75 years and older.
Earlier Friday, de Blasio renewed his call for the expansion, saying the city has 270,000 unused doses that could go to people over 75 -- of which the city is home to 560,000.
"We've got literally twice as many New Yorkers over 75 than the amount of vaccine we have in stock, but yet we are not allowed by state law to give a single shot to a single New Yorker over 75," de Blasio said. "I guarantee you, if these standards are changed by the state, we are going to run through those 270,000 doses very, very quickly. Again, if we are given approval by the state, we will run through those 270,000 doses very quickly because we have so many people who want it."
De Blasio also announced that five new vaccination sites will be open Monday -- one in each of the five boroughs-- to vaccinate members of the 1b group.
Additionally, the Javits Center will open as a vaccine distribution site on Wednesday.
Meantime, Police Commissioner Dermot Shea tested positive for COVID-19, along with 463 NYPD members who have tested positive for coronavirus this month.
Those qualified can register for a vaccine on the city's website. Starting on Monday, a phone-in reservation system will also be up and running.
CHECK THE LIST of who is eligible for a vaccine in New York State
MORE CORONAVIRUS COVID-19 COVERAGE
Coronavirus by zip code - New York City
COVID Vaccine Calculator: Find out how many people may get a COVID-19 vaccine before you
Do you have coronavirus symptoms?
Where to get tested for COVID-19 coronavirus
WATCH: Eyewitness to a Pandemic
New York City
Westchester and Hudson Valley
Centers for Disease Control and Prevention on coronavirus
Submit a News Tip