Republican Gov. Matt Bevin conceded a tight Kentucky gubernatorial race after a formal review of county vote totals in last week’s election, making Democrat Andy Beshear the winner by roughly 5,000 votes.

As part of the recanvass Thursday, the state’s 120 counties rechecked the vote totals they submitted to the state, but didn’t conduct a recount of individual ballots. The results showed virtually no change—leaving Mr. Bevin unable to overcome the 5,189-vote margin, out of more than 1.4 million ballots cast, that Mr. Beshear...