Gov. Cuomo approved a new policy Tuesday night allowing impoverished transgender New Yorkers to bill taxpayers for sex-change surgery.

The Cuomo administration issued new rules requiring New York’s highest-in-the-nation $55 billion Medicaid program — the government health-insurance program for the needy — to foot the bill for “gender reassignment” operations.

State officials estimate the expanded coverage for transgender operations and services will cost the Medicaid program $6.7 million a year.

There are 353 men and 308 women on Medicaid who have been diagnosed with gender-identify disorder.

The state Department of Health estimated that a portion of these individuals will seek either hormone therapy or reassignment surgery.

The cost for sex-change operations — which include testicle removal, breast augmentation and mastectomy — ranges from $15,000 to $50,000. That doesn’t include thousands of dollars in therapy and counseling services.

Medicaid will pick up the tab for transgender New Yorkers who are over 18, although the patients must be 21 to get surgery that results in sterilization.

‎“New York state has always been a progressive leader and ensuring that all New Yorkers — regardless of gender identity — are treated fairly will continue this legacy,” Cuomo said.

“This new regulation will guarantee transgender New Yorkers access to Medicaid-funded care, which is critical to safeguarding the principle of equal treatment,” he said.

“I am proud that the state is taking this step and continuing to lead the fight on transgender rights.”

New York joins ‎ Oregon, Massachusetts, Vermont, Washington, DC, and Maryland in offering medical services to transgender residents.

But Republican leaders slammed Cuomo’s move as outrageous.

“Sometimes you just have to say ‘no,’ and this is clearly one of them,” said Westchester County Executive Rob Astorino.

“New Yorkers pay the highest ‎property taxes in America because our Medicaid costs already are through the roof, Putting taxpayers on the hook for sex change operations when they often struggle to pay for their own basic health-care needs is ridiculous, no matter how it’s spun,” he said.

State Sen. Martin Golden (R-Brooklyn) predicted the Medicaid costs for sex-change operations will be much higher.

“The state is saying it will cost $67 million over ten years. It will be over $100 million. It’s an inappropriate use of taxpayer dollars,” Golden said.

Cuomo’s move also will make it easier for foster-care residents in the city’s care who identify as transgender to get sex-reassignment surgery through Medicaid. The city — as well as the state — has been sued for discrimination after refusing to pay for such services.

“We look forward to working with the State in the implementation and roll out of these critical and lifesaving health care provisions for the transgender community,” Speaker Melissa Mark Viverito and the Council’s LGBT Caucus said in a join statement.

“We applaud the Cuomo administration for taking this important step,” said Michael Silverman, director of the Transgender Legal Defense & Education Policy. “New York is poised to become a model state when it comes to the protection of its transgender residents.”

But Silverman objected to Cuomo limiting the transgender services to adults while continuing to exclude youths.