The New York Times declared Portman, a former congressman who was President George W. Bush's budget director, defeated Lt. Gov. Lee Fisher, the Democratic nominee.
Portman takes the seat being given up by Sen. George Voinovich, a Republican.
The Youngstown Vindicator said Portman's final tally was 2,069,410 votes to 1,419,281 for Fisher.
The newspaper said incumbent Democratic Gov. Ted Strickland lost to Republican John Kasich, a former congressman, in his bid for another term, 1,730,744 to 1,822,681.
In five of the state's 18 House races, incumbent Democrats lost to Republican challengers, bringing the totals to 13 seats for the GOP and five for the Democrats.
President Barack Obama and Vice President Joe Biden both campaigned for the Democratic candidates in the final days of the campaign.