Stores that sell ammunition will have to register with the state, run background checks on buyers of bullets and keep an electronic database of bullet sales.
In another provision, a therapist who believes a mental health patient made a credible threat to use a gun illegally would be required to report it to a mental health director who would have to notify the state. A patient's gun could be taken from him or her.
The legislation also increases sentences for gun crimes including the shooting of a first responder that Cuomo called the "Webster provision." Last month in the western New York town of Webster, two firefighters were killed after responding to a fire set by the shooter, who eventually killed himself.
The measure passed the Senate 43-18 on the strength of support from Democrats, many of whom previously sponsored bills that were once blocked by Republicans. The Democrat-led Assembly gaveled out before midnight and planned to take the issue up at 10 a.m. Tuesday. It is expected to pass easily.
The governor confirmed the proposal, previously worked out in closed session, also would mandate a police registry of assault weapons, grandfathering in assault weapons already in private hands.
It was agreed upon exactly a month since the Sandy Hook Elementary School tragedy.
"It is well-balanced, it protects the Second Amendment," said Senate Republican leader Dean Skelos of Long Island.
Cuomo said he wanted quick action to avoid a run on assault weapons and ammunition. He estimates there are already about 1 million assault weapons in New York state.
Republican Sen. Greg Ball called that political opportunism in a rare criticism of the popular and powerful governor seen by his supporters as a possible candidate for president in 2016.
"We haven't saved any lives tonight, except one: the political life of a governor who wants to be president," said Ball who represents part of the Hudson Valley. "We have taken an entire category of firearms that are currently legal that are in the homes of law-abiding, tax paying citizens. ... We are now turning those law-abiding citizens into criminals."