The "Compassionate Care Act" was passed by the State Assembly early Friday, according to Jason Elan, a spokesman for Sen. Diane Savino, a sponsor of the bill. The state Senate later passed the bill.
Under the proposed law, doctors will be allowed to prescribe marijuana in a non-smokable form to patients with serious diseases and conditions that are recognized by the state on a predefined but flexible list of conditions.
On Friday, Cuomo reiterated his support for the measure, which could take up to 18 months to fully implement.
"Medical marijuana has significant upsides and significant potential downsides," Cuomo told reporters. "We wanted to do right. And that was the balance that we had to find in this piece of legislation... It is a system that will provide the benefits to people who need it, which can be significant. Even for children, children with epilepsy. But it is a system that also has safeguards, will involve the State Police to monitor and supervise the system."
In a statement, Savino, who represents New York City, called the measure "an historic victory for thousands of New Yorkers who will no longer have to suffer needlessly during their courageous medical battles."
"Under this bill, New Yorkers will now have the same access to life-changing treatment options that others around the country have had," she added.
The legalization of medical marijuana has had "overwhelming support" in state polls, State Assembly speaker Sheldon Silver said in a statement.
The day before the bill was passed, Cuomo said the it includes criminal penalties in case a person tries to defraud the system, as well as a "fail safe" mechanism allowing the governor to "suspend the program at any time on recommendation of either the State Police Superintendent or the Commissioner of Health if there is a risk to the public health or public safety."
New York will be the 23rd state, along with the District of Columbia, to allow medical marijuana in some form, according to information compiled by the National Conference of State Legislatures
Among the states that allow medical marijuana are Connecticut, Vermont and New Jersey, each of which border New York.
The momentum has picked up recently, with most of these efforts taking effect over the past decade.
A proponent of the measure, Missy Miller of Long Island, said she considered moving to California to gain access to a special strain of marijuana called Charlotte's Web oil, a derivative that may help cease her son Oliver's seizures.
Oliver, 14, suffered a stroke in utero that resulted in a brainstem injury. Among several other life-threatening consequences are seizures, sometimes more than a dozen a day.
"I am extremely relieved and proud to have been a part of helping bring necessary change that so many of us need," Miller said.
But "I am quite concerned about the 18-month implementation, though, because Oliver does not have that time to wait. I am hopeful that some kind of expedited access plan can be worked out to help those with urgent need like Oliver."
Opponents of the measure have said it driven by politics.
"I think serious questions can be raised about using a political vehicle to achieve the use of a prescribable medication in America," William Foster, president of the National Council on Alcoholism and Drug Dependency, told CNN when the plan was unveiled in January.