The measure now heads to Democratic Gov. Mike Beebe, who plans to sign it into law. The measure needed at least 75 votes in the 100-member House.
The program's future had been in doubt after failing to win enough support four days in a row in the state House last month. The state Senate had approved the funding measure without a vote to spare.
The plan has sharply divided Republicans, and the votes will likely continue to be an issue in GOP primaries for legislative, statewide and congressional offices in May. Republicans control the Legislature and have made major gains in Arkansas over the past two elections by running against President Barack Obama's healthcare law.
Despite that push against the law derided as "Obamacare," top Republicans in the Legislature were the architects and biggest advocates of the private option. They argued that private insurers could provide services more efficiently than the government, and they cast it as a way to reform Medicaid.
GOP opponents said the private option was no different than embracing the president's health law, and they said the state couldn't afford the 10% cost it would eventually have to contribute.
National health policy experts say Arkansas' compromise opened the door for other Republican-leaning states to consider similar models. Other states exploring or pursuing similar ideas include Pennsylvania, Iowa and Virginia.
Beebe has said rejecting the $915 million in federal funds for the private option would jeopardize other state services. Beebe's proposed $5 billion budget relies on $89 million in savings he says the private option will create by cutting down on hospitals' uncompensated care costs.
Supporters have spent the past week talking with a handful of private option opponents, who had floated the idea of backing the bill if state officials agreed to try to limit the enrollment period for it.