As part of the standard protocol, DeWine was tested for COVID-19 before he was scheduled to meet with Trump. The state's lieutenant governor, Jon Husted, tested negative for the virus.
The governor, who's returning to Columbus with his wife, currently has no COVID-19 symptoms, his office said in a news release.
The Republican governor plans to self-quarantine at his home in Cedarville for the next 14 days. He is the second U.S. governor to test positive for the virus.
“The president wishes Gov. DeWine a speedy and full recovery and commends the job he’s doing for the great state of Ohio," White House deputy press secretary Judd Deere said in a statement.
DeWine was one of the first governors to take drastic measures in trying to mitigate the spread of the virus. The Buckeye State was the first nationwide to close all schools in the face of the outbreak.
As of Wednesday, Ohio had 91,171 confirmed cases of the virus, according to the state health department. About 3,326 individuals in the state have died of the disease.
Fox News' Matt Leach contributed to this report