At issue was whether the process used by the state violated the National Voter Registration Act (NVRA) of 1993, or the more recent Help America Vote Act (HAVA).
Each state has a process for removing voters believed to have moved from its registration lists. He is joined by his four conservative colleagues.
Half a dozen other states have similar practices.
In the past, the Justice Department has opposed Ohio's process as inconsistent with federal law.
The majority rejected the silly argument that because OH uses the absence of "voter activity" to trigger the removal process, it violates the requirement that a state purge "shall not result in the removal of the name of any person.by reason of the person's failure to vote".
But the Supreme Court majority said the appeals court was wrong because Ohio's process does not conflict with federal directives. But other states may now follow Ohio's lead.
The court's dissenters said OH violates a prohibition in federal law against removing voters simply because they are exercising their right not to vote. If there was a clearly, solidly established presumption in favor of the right to vote and a difficult set of obstacles for would-be vote suppressors to overcome, decisions like this would be hard to write. And of course, they're all red states.
Supreme Court rules Ohio's voter purge didn't...
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Under Ohio's policy, if registered voters miss voting for two years, they are sent registration confirmation notices. As part of the lawsuit, a judge previous year ordered the state to count 7,515 ballots cast by people whose names had been removed from the voter rolls.
Reminder: In #Husted, the Department of Justice under Jeff Sessions made a decision to abandon its longstanding position that the National Voter Registration Act and the Help America Vote Act prohibit techniques like Ohio's voter purge. Utah removed 76,000 voters in 2012 - including 60,000 in Salt Lake County alone, the one Democratic bastion in an otherwise deeply conservative state.
The case was Husted v. A. Philip Randolph Institute.
Justice Sonia Sotomayor, in addition to joining Breyer's dissent, wrote separately to emphasize her belief that the majority's interpretation ignores the intent of the motor voter law - to expand, not restrict, voter participation. A federal appeals court had blocked the procedure for 2016, letting 7,500 state residents cast ballots even though they'd previously been struck from the rolls.
Justice Sotomayor, in addition to joining the main dissent, also wrote separately to emphasize how voter purge schemes like Ohio's have a disproportionate impact on low-income voters and minority voters.
If they do not respond to the notice or do not vote over the next four years, they are dropped from the registration rolls.
The litigation also marked one of several high-profile matters in which the Justice Department in the Trump administration sharply reversed course from its positions in the Obama era.
Husted said that OH wants to "make it easy to vote and hard to cheat". Ohio's process, he claims, "does not strike any registrant exclusively by reason of the failure to vote".