The governor’s action also comes as advocates for changing drug laws have stepped up criticism of New York City’s stringent enforcement of marijuana laws, which resulted in nearly 450,000 misdemeanor charges from 2002 to 2012, according to the Drug Policy Alliance, which advocates more liberal drug laws.

During that period, medical marijuana became increasingly widespread outside New York, with some 20 states and the District of Columbia now allowing its use.

Mr. Cuomo voiced support for changing drug laws as recently as the 2013 legislative session, when he backed an initiative to decriminalize so-called open view possession of 15 grams or less. And though he said he remained opposed to medical marijuana, he indicated as late as April that he was keeping an open mind.

His shift, according to a person briefed on the governor’s views but not authorized to speak on the record, was rooted in his belief that the program he has drawn up can help those in need, while limiting the potential for abuse. Mr. Cuomo is also up for election this year, and polls have shown overwhelming support for medical marijuana in New York: 82 percent of New York voters approved of the idea in a survey by Siena College last May.

Still, Mr. Cuomo’s plan is sure to turn heads in Albany, the state’s capital. Medical marijuana bills have passed the State Assembly four times — most recently in 2013 — only to stall in the Senate, where a group of breakaway Democrats shares leadership with Republicans, who have traditionally been lukewarm on the issue.

Mr. Cuomo has decided to bypass the Legislature altogether.

In taking the matter into his own hands, the governor is relying on a provision in the public health law known as the Antonio G. Olivieri Controlled Substance Therapeutic Research Program. It allows for the use of controlled substances for “cancer patients, glaucoma patients, and patients afflicted with other diseases as such diseases are approved by the commissioner.”

Mr. Olivieri was a New York City councilman and state assemblyman who died in 1980 at age 39. Suffering from a brain tumor, he used marijuana to overcome some of the discomfort of chemotherapy, and until his death lobbied for state legislation to legalize its medical use.