Hanks and Wilson, both 63, sought medical advice after experiencing symptoms of a cold in Queensland, the actor wrote on Instagram.
They will now spend time in isolation, he added.
The US couple had been on the Gold Coast, where Hanks was working on a film about the life of Elvis Presley.
On Wednesday, the World Health Organization (WHO) officially declared the outbreak to be a pandemic.
Hanks wrote on Instagram: “We felt a bit tired, like we had colds, and some body aches. Rita had some chills that come 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”.
The Academy Award winner, whose films include Forrest Gump and Saving Private Ryan, said they would keep the world “posted and updated”.
“We Hanks’ will be tested, observed, and isolated for as long as public health and safety requires. Not much more to it than a one-day-at-a-time approach, no?”
The studio making the film, Warner Bros, said: “The health and safety of our company members is always our top priority, and we are taking precautions to protect everyone who works on our productions around the world.”
Local media reported that work on the untitled movie, directed by Australian Baz Luhrmann, had been temporarily suspended.
Wilson, a singer and actress, has performed concerts at Brisbane’s Emporium Hotel and the Sydney Opera House in the past week.