The measure, which passed the Assembly 104-43, also calls for restrictions on ammunition and the sale of guns.
"This is not about taking anyone's rights away," Democratic Sen. Jeffrey Klein said when the bill passed the Senate late Monday. "It's about a safe society ... today we are setting the mark for the rest of the county to do what's right."
Under current state law, assault weapons are defined by having two "military rifle" features such as folding stock, muzzle flash suppressor or bayonet mount. The proposal reduces that to one feature and includes the popular pistol grip.
Private sales of assault weapons to someone other than an immediate family will be subject to a background check through a dealer. New Yorkers also would be barred from buying assault weapons over the Internet, and failing to safely store a weapon could lead to a misdemeanor charge. (Read More:
Here's What New York State's New Gun Law Would Do
Ammunition magazines will be restricted to seven bullets, from the current 10, and current owners of higher-capacity magazines will have a year to sell them out of state. An owner caught at home with eight or more bullets in a magazine will face a misdemeanor charge.
Another provision places requirements on therapists, psychologists, registered nurses and licensed social workers who believe a mental health patient made a credible threat to use a gun illegally. They would be required to report such a threat to a mental health director, who would have to notify the state. Any registered handguns -- or registered assault weapons purchased before the ban -- could be taken from the patient.
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 governor confirmed the proposal, previously worked out in closed session, also mandate a police registry of assault weapons, grandfathering in the estimated 1 million assault weapons already in private hands.
It was agreed upon exactly a month since the Sandy Hook Elementary School tragedy in neighboring Connecticut.
"It is well-balanced, it protects the Second Amendment," said Senate Republican leader Dean Skelos.
Cuomo said he wanted quick action to avoid a run on assault weapons and ammunition.
Assemblyman Steve Katz said legislators were being "bullied." He said the bill is "solely for the governor's egotistical, misguided notion."
Republicans argued the bill wouldn't stop mass shootings or other gun crimes but instead turns law-abiding into potential criminals.
Republican Assemblyman James Tedisco said the bill was dangerous because it would give people a "false sense of well-being."