A representative for the couple confirmed they are now in self-isolation at a rented home in Australia.
Tom and Rita, who have been married for more than 30 years, announced they had been diagnosed with Covid-19 last week, contracting the virus while working Down Under.
Tom, 63, had been filming Baz Luhrmann’s as-yet untitled Elvis Presley biopic for Warner Bros, in which he will play the singer’s manager Colonel Tom Parker.
Following his diagnosis, production on the film was halted.
There are currently 375 confirmed cases of the virus in Australia.
Tom had previously offered thanks to “the helpers” while he was in hospital.
He shared a photo of a stuffed kangaroo and koala and a piece of toast thickly spread with Australian staple Vegemite.
Tom and Rita are not the only high-profile stars to test positive for Covid-19.
On Monday, Idris Elba told fans he had the virus, but said he feels “OK” and does not have any symptoms.