ObamaCare is going to push 300,000 additional New Yorkers onto the Medicaid rolls by next year — a hefty 7.3 percent increase, Gov. Cuomo’s budget office predicts.

Cuomo’s mid-year budget report says Medicaid rolls will swell from the current 5.3 million to more than 5.6 million by the end of 2014.

The reason: Many uninsured and low-income New Yorkers signing up for coverage on the state-run ObamaCare Web site will discover they’re eligible for Medicaid, the public health-insurance program for the needy.

Following a state review, residents whose incomes qualify for Medi­caid are then enrolled.

For many, it’s like hitting the jackpot: free health care.

State officials estimate that 1 million uninsured New Yorkers are Medicaid-eligible. That means the number of residents who sign up for Medicaid over the next several years could soar to more than 6 million — nearly one third of the Empire State’s population, officials said.

Since the Oct. 1 rollout of the ­Affordable Care Act in New York, nearly half of New Yorkers who signed up for insurance on the state-run exchange qualified for Medicaid.

Of the 76,177 sign-ups, 46 percent were Medicaid enrollees, while 41,021 enrolled in commercial plans. Many of those with moderate incomes who obtain private insurance are also eligible for public subsidies to help cover their premiums.

Cuomo has welcomed the Medicaid expansion because under ObamaCare the federal government is financing most of the costs of new enrollees.

Traditionally, the feds and New York state and local governments split the costs of the state’s massive, $55 billion Medicaid program, the largest in the nation.

Starting in 2014, the feds will pick up 75 percent of the tab and eventually 90 percent for childless Medicaid adults, instead of the current 50 percent. The new law expands eligibility for single adults to 130 percent of the poverty level, from the present 100 percent.

The new formulas will save New York state $2.3 billion a year.

Health advocates said the Medicaid expansion thus far has been the brightest spot in the ObamaCare rollout — at least in states that have agreed to participate.

“We’ve made good progress. ­Enrolling uninsured residents into Medicaid has been an important policy goal of New York for a long time,” said Assembly Health Committee chairman Richard Gottfried (D-Manhattan).

“Enrolling people in Medicaid makes economic sense. It means fewer expensive, unpaid hospital bills and a healthier workforce. It’s health care, not welfare,” he said.