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 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".
He 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?"
Hanks, 63, is set to play Colonel Tom Parker in Luhrmann's Elvis film that is in preproduction on Australia's Gold Coast.
On March 5, Wilson performed songs from her new album Halfway to Home at Brisbane's Emporium Hotel. On Saturday, Wilson made her debut at the Sydney Opera House. It is not yet known if Wilson was infectious then.
The news broke just as US President Donald Trump announced a 30-day suspension on travel from Europe to the United States due to the spread of coronavirus. Earlier on Wednesday, the World Health Organization officially declared COVID-19 a global pandemic.
There have been more than 115,000 cases of coronavirus confirmed worldwide, and the disease has killed more than 4,200 people.
Get all latest content delivered to your email a few times a month.
Bringing Pop Culture News from Every Realm, Get All the Latest Movie, TV News, Reviews & Trailers
Got Any questions? Drop an email to [email protected]