According to the briefing, the 71-year-old "has been displaying mild symptoms, but otherwise remains in good health and has been working from home throughout the last few days as usual."
Based on the results of the tests, the Duke and Duchess of Cornwall are following medical and government advice and self-isolating separately.
"In accordance with government and medical advice, the Prince and the Duchess are now self-isolating at home in Scotland," the statement continues. "The tests were carried out by the NHS in Aberdeenshire where they met the criteria required for testing."
Charles and Camilla are reportedly in self-isolation at their Birkhall home at the Royal Family's Balmoral estate. It is believed they will remain there for the foreseeable future, according to Town & Country.
The BBC reported that Birkhall isn't a "huge house but certainly big enough to isolate yourself within it" and the couple also have staff to support them.
Buckingham Palace has also released a statement, reporting the Queen remains in good health. She left Buckingham Palace for Windsor Castle on March 19.
Charles is the first member of the British Royal Family to test positive for COVID-19. Other members from European royal families have also tested positive for the novel coronavirus.
Last week, Karl von Habsburg, the ancestral Archduke of Austria, became the first royal to test positive. Prince Albert of Monaco revealed he had contracted the coronavirus a few days later. Thankfully, both only exhibited mild symptoms, like Charles.
Earlier this month, Camilla attended the 2020 Cheltenham Festival, along with Princess Anne, Zara and Mike Tindall and Peter and Autumn Phillips. She was on hand to award trophies to some of the trainers and participants.