ABC News says the veteran newsman intends to continue anchoring "Good Morning America" from his home.
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In a statement, ABC wished him a "healthy and speedy recovery."
His wife, Ali Wentworth, earlier tested positive for the virus. She has been recovering.
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Stephanopoulos said on GMA Monday that he appears to be asymptomatic.
"I've never had a fever, never had chills, never had a headache, never had a cough, never had shortness of breath," he said. "I'm feeling great."
He also said his wife's condition is improving.
Dr. Jennifer Ashton, ABC News chief medical correspondent, noted at the time of Wentworth's diagnosis that Stephanopoulos and his family were practicing the "home version of social distancing" that must be done when a person in the household tests positive for COVID-19.