A three-judge panel of the 6th Circuit had disagreed last week. The full court's ruling, in which nine of 16 judges concurred, 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 presidential primary election last March between Sens. Barack Obama and Hillary Rodham Clinton. The presidential election is Nov. 4.
Since the primary, 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 sufficient systems exist to verify new voter registrations and there was no way to set up the court-ordered system with such speed.
Last week, the three-judge panel of the 6th Circuit had sided with Brunner, but the full panel sided with the GOP and U.S. District Judge George C. Smith in Columbus after hearing an appeal. Smith had ordered Brunner to develop a way to verify voter registration information and make it available to local election boards.
The federal appeals court ruled Tuesday that the current system "is essentially useless - not unlike asking for a drink of water and being given access to a fire hose at full volume - and will do nothing to address the anti-fraud objective."
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.
"As far as we can tell, the problem with the current system is not that it is insufficiently user-friendly but that it is effectively useless," the majority said in its ruling.
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.
Elsewhere in the state, the state GOP has requested information on voters in Licking County, in central Ohio, who registered and cast an early ballot on the same day during a weeklong period. The request is similar to one made last week by the Republican sheriff of Greene County that infuriated Democrats and voting rights groups, and was withdrawn a day later.
The GOP has said it is concerned that the same-day voting period could have made it easier to commit voter fraud.
Associated Press writer Stephen Majors contributed to this report.