"New York is once again leading the way to prevent gun violence, and with this common sense reform, break the inextricable link between gun violence and domestic violence," Cuomo said. "This legislation builds on our gun laws -- already the strongest in the nation -- to make New York safer and stronger."
The changes in the law included adding a list of serious misdemeanors.
Firearms were used in 35 domestic killings in the state in 2016, the governor's office said.
The law also can prevent someone from getting or renewing a license for a gun if the person is the subject of an arrest warrant for certain alleged crimes.
The governor said the state wants its laws to prevent dangerous people from getting weapons.
"Legitimate gun owners can still own a gun," Cuomo said.
The measure passed 41-19 in the Senate and 85-32 in the state Assembly.