BBC royal correspondent Nicholas Witchell says the prince and his wife flew to Scotland on Sunday, although they did not travel on a scheduled flight.
He adds that they were both tested on Monday and got their results last night.
Prince Charles’s last public engagement was on 12 March – the same day he last saw his mother, the Queen. Palace officials say the Monarch remains in “good health”.
The prince, 71, and his wife, the Duchess of Cornwall, 72, are self-isolating at Birkhall on the Balmoral Estate in Aberdeenshire.
A Palace statement said: “The tests were carried out by the NHS in Aberdeenshire where they met the criteria required for testing.”
The Prince of Wales has tested positive for coronavirus, Clarence House has confirmed.
Prince Charles, 71, is displaying mild symptoms “but otherwise remains in good health”, a spokesman said.
The Duchess of Cornwall, 72, has also been tested but does not have the virus.
Clarence House said Charles and Camilla were now self-isolating at Balmoral, adding the prince “has been working at home throughout the last few days”.
An official statement read: “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.”