President Biden finalized a new policy Friday giving illegal immigrant “Dreamers” here under the DACA program full access to Obamacare, including taxpayer subsidies to buy insurance on the Affordable Care Act’s markets.

Mr. Biden is redefining what it means to be in the country lawfully, at least for purposes of Obamacare, so it now includes DACA recipients.

Those in DACA were already able to buy plans on their own, under a previous Biden change. But they now can access government money to buy coverage.

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The move unwinds a wall erected by President Obama when he created Deferred Action for Childhood Arrivals in 2012. Wary of asking taxpayers to pay for illegal immigrants’ benefits, he made a policy decision to exclude DACA recipients.

Mr. Biden, who was vice president at the time, now treats that decision as a mistake and says DACA migrants deserve the same right to government health-care money as anyone else.

“Dreamers are our loved ones, our nurses, teachers and small business owners. And they deserve the promise of health care just like all of us,” the president said.

Xavier Becerra, secretary of Health and Human Services, spoke similarly and called them “fellow Americans.”

“Dreamers are our neighbors and friends; they are students, teachers, social workers, doctors, and nurses. More importantly, they are fellow Americans,” he said.

The administration figures that 100,000 DACA recipients will take advantage of the free money.

There are roughly 600,000 people enrolled in the DACA program, but many of them already have insurance coverage through their jobs, some qualify for Medicaid under states that have expanded coverage to illegal immigrants, and others will decline to sign up.

The new policy will take effect Nov. 1, just before the election and the start date in most states for the next Obamacare open enrollment period.

Mr. Obama first announced DACA 12 years ago, months before the 2012 election, at a time when he was struggling with Hispanic voters. Given the demographics of illegal immigrants, most DACA recipients are Hispanic.

Now it is Mr. Biden who is struggling with Hispanic voters.

DACA grants a stay of deportation to illegal immigrants who arrived in the U.S. under age 16 and were under age 31 when the policy was announced. Most of those who qualify were never high targets for deportation anyway, so the real benefit to DACA is the work permit and taxpayer benefits that come with the program.

Administration officials said other migrants here in the U.S. under deferred action have already been eligible for Obamacare and Friday’s policy brings DACA into line.

President Trump tried to end DACA but was blocked by the courts. At the same time, courts have also ruled the original DACA policy itself illegal, though that ruling is on hold while appeals wind their way through the process.

Administration officials declined to speculate on whether the new definition of lawful presence will have implications for the legal battle.

They said that the change in definition doesn’t affect other areas where DACA recipients are still considered here unlawfully, such as Medicaid.