A three-judge panel of the 6th Circuit had disagreed last week, but the full court's ruling overturns that decision.
Ohio Republicans had sued Brunner, a Democrat. Her spokesman had no immediate comment Tuesday.
About 666,000 Ohioans have registered to vote since January, with many doing so before the contested Democratic primary election last March between Sens. Barack Obama and Hillary Rodham Clinton.
Since then, Ohio Republicans have filed a series of challenges to the registrations and Brunner's administration of election rules. They have helped voters file lawsuits against local boards of election over registration rules, absentee ballot requests and a weeklong period that allowed registration and voting on the same day.
Brunner previously said there was no way to set up the system with such speed.
Last week, a three-judge panel of the 6th Circuit had sided with Brunner, but after hearing an appeal the full panel sided with the GOP and U.S. District Judge George C. Smith in Columbus. Smith had ordered Brunner to develop a way to verify voter registration information and make it available to local election boards.
Brunner argued that it would take two to three days to create the necessary computer programs, and said nothing in the federal Help America Vote Act required her to do what the district court ordered.
Tuesday's order directs Brunner to verify new registrations by comparing that information with data from the Ohio Bureau of Motor Vehicles or the Social Security Administration.
Ohio Republican Chairman Bob Bennett accused Brunner of pursuing a partisan agenda and said "her delay in providing this matching system leaves little time for election officials to act on questionable registrations.
Bennett said Brunner was destroying the public's trust in Ohio's elections system.
"Her shameful actions to disenfranchise Republican absentee voters, block the transparency of early voting and refuse the proper verification of newly registered voters have rightfully damaged her credibility as a nonpartisan election administrator," he said.
Polling in the state shows Obama, now the Democratic presidential nominee, slightly ahead of Republican challenger John McCain. Both campaigns have worked hard in the state, which has 20 electoral votes and gave President Bush a second term in 2004.