ALBANY — Nassau County will transfer its authority to install 1,000 video slot machines to Aqueduct Racetrack in Queens in exchange for annual payments that will total at least $43 million over the first three years, under a provision being tucked into the state budget agreement, lawmakers said late Wednesday.

The deal would resolve thorny problems for the county, Nassau Off-Track Betting Corp. and Aqueduct.

The arrangement would solve Nassau’s problem of finding a location for a video slots parlor — which has been met with staunch opposition at more than one proposed site — while guaranteeing the county a revenue stream through OTB. Further, it alleviates Aqueduct’s concern with facing slots competition from nearby Belmont Park, the racetrack where Nassau recently proposed to use for slots.

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Under the proposed terms, Genting New York LLC, which operates the Resorts World casino at Aqueduct, would get the authority to add 1,000 “video lottery terminals” to the 5,400 it already has at the track.

Resorts World would pay Nassau County Off-Track Betting $9 million in 2016, $9 million in $2017 and $25 million in 2018. Future payments would be $25 million plus an amount adjusted for inflation, officials said.

“It’s a fantastic deal,” said Sen. Jack Martins (R-Old Westbury), who helped negotiate the agreement. “It’s a deal that works for all sides. Nassau County gets the benefit of the revenue stream without having the facility in Nassau. … Obviously, no place in Nassau County was willing to take the VLTs, so at some point, we had to realize that and, frankly, this was a great opportunity.”

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The transfer would be included as part of a state budget deal lawmakers are negotiating at the State Capitol. They were trying to finalize it by Thursday.

“If we have a state budget, this will be in it,” Martins said.

Nassau County Executive Edward Mangano called it a “good resolution.”

Opponents of the Belmont casino expressed relief at the deal.

Assemb. Michaelle Solages (D-Elmont), who sponsored legislation to kill the VLT authority, said the agreement “balances the need for revenue with the need to protect the community.”

Solages and Assemb. Todd Kaminsky (D-Long Beach), who also opposed slots at Belmont, called the outcome a “win-win.”

“We stood with the people of Nassau County to tell Albany we didn’t want their casino in Belmont — and our voices were heard loud and clear,” they said in a joint statement. “Not only will the communities around Belmont Park be spared from a wrongheaded plan to put a VLT casino there, Nassau County will gain a substantial revenue stream from one of the most profitable casinos in New York City.”

Matthew Sexton of Floral Park, who led rallies and circulated petitions to block the casino, said the agreement “shows that all parties can work together to find solutions that benefit everyone.”

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Laura Ferone, president of the Floral Park-Bellerose school district, said the deal allows Resorts World to remain successful while “preserving the county.”

A Nassau OTB spokesman said partnering with Genting “ensures a long term and vital revenue stream for Nassau.”

Floral Park Mayor Thomas Tweedy, a vocal critic, called the agreement “the best possible deal for Nassau County and its residents.” Nassau and Suffolk counties received authority to operate up to 1,000 video slot machines under a 2013 gambling-expansion law. But the counties have run into road blocks with proposed sites.

Nassau OTB first selected the vacant Fortunoff building in Westbury, but abandoned it after a wave of protests. Last fall, OTB switched its sites to Belmont, figuring slots would be compatible at a horse racing track. But again, neighbors have held vocal rallies denouncing the proposal. Meanwhile, the county has been missing out on tens of millions of dollars in potential revenue.