Northam, a Democrat, had urged lawmakers to move quickly to approve additional funding for absentee voting, with the presidential election just two months away.
States around the country are expecting a big increase in voting by mail because of the ongoing health threat from the coronavirus.
Republican President Donald Trump has sharply criticized the Postal Service, which he considers wasteful, and has threatened to oppose extra money to help it handle record levels of mail-in ballots.
Some Republicans in Virginia have objected to spending $2 million on postage and questioned whether the drop boxes to be placed at polling places and other locations will be secure enough to prevent voter fraud.
Democrats have argued that the pandemic calls for unprecedented action to ensure voting is as easy as possible for every eligible voter.
The legislation requires that cities and counties provide the prepaid postage for voters to mail in their absentee ballots, but they will be reimbursed by the state Department of Elections.
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