Video report by ITV News Royal Editor Chris Ship
The Duchess of Cornwall has also been tested but does not have the virus.
A source said both remained in good spirits and that the prince was up and about and not bedridden, while the medical advice is that it is unlikely to escalate into a more serious case.
Buckingham Palace have said the Queen "remains in good health" and last saw Charles on the morning of March 12.
The Duke of Edinburgh was not with the Queen at Buckingham Palace when she last met Charles, the palace confirmed.
The prince travelled to Birkhall on Sunday before he was tested on Monday and they are both now self-isolating at the Burnham on the Balmoral Estate in Scotland.
In a statement, Clarence House said: “The Prince of Wales has tested positive for coronavirus.
"He has been displaying mild symptoms but otherwise remains in good health and has been working from home throughout the last few days as usual.
“The Duchess of Cornwall has also been tested but does not have the virus. In accordance with Government and medical advice, the Prince and the Duchess are now self-isolating at home in Scotland.
“The tests were carried out by the NHS in Aberdeenshire where they met the criteria required for testing.
“It is not possible to ascertain from whom the Prince caught the virus owing to the high number of engagements he carried out in his public role during recent weeks.”
Charles's last public engagement was on March 12, but he did have a number of private meetings with Highgrove and Duchy individuals, all of whom have been made aware.
Prince Albert of Monaco, who tested positive earlier this month, was in the same room as Charles at a WaterAid event in London on March 10.
Charles is not believed to have shaken hands with Prince Albert.
A source said his doctor's most conservative estimate was that Charles was contagious on March 13.
A small number of people living and working at Birkhall are remaining at the residence and self-isolating.
Charles has spoken to his sons the Duke of Cambridge and the Duke of Sussex, as well as the Queen.
Coronavirus: Everything you need to know