The 63-year-old Forrest Gump star revealed the shock diagnosis on Thursday, sharing a photo of a pair of gloves in a cytotoxic rubbish bin.
The couple tested positive while in the Gold Coast, where Hanks is about to start filming a flick.
“We felt a bit tired, like we had colds, and some body aches. Rita had some chills that came and went. Slight fevers too.
“To play things right, as is needed in the world right now, we were tested for the Coronavirus, and were found to be positive.”
After the announcement, Campbell went into self-isolation.
Speaking on 2GB's Afternoons with Deborah Knight, he revealed: "I interviewed her on Monday, Deb. She came into the Today Extra studios on Monday and she was delightful and really nice and she didn't have any symptoms of anything."
He added: "She was cautious. She actually made a joke coming into the studios, saying we shouldn't shake hands, we should bump elbows. So we bumped elbows."
David and his Today Extra co-host Belinda Russell, who was also on the panel when they interviewed Rita, are both taking precautionary measures.
Hanks has since given fans an update on he and wife Rita's diagnosis.
The Hollywood legend took to Instagram on Friday to let fans know that he and his wife are "taking it one day at a time".
"Rita Wilson and I want to thank everyone here Down Under who are taking such good care of us," he wrote on Instagram.
"We have Covid-19 and are in isolation so we do not spread it to anyone else. There are those for whom it could lead to a very serious illness. We are taking it one-day-at-a-time.
"There are things we can all do to get through this by following the advice of experts and taking care of ourselves and each other, no? Remember, despite all the current events, there is no crying in baseball. Hanx."