Their plane landed just before 12.30pm, having taken off from RAF Northolt in Hillingdon, west London.
They were met by Scotland’s First Minister Nicola Sturgeon and the Lord Provost of the City of Edinburgh Robert Aldridge.
While Camilla got into the waiting car, Charles briefly spoke with Secretary of State for Scotland Alister Jack, Police Scotland chief constable Sir Iain Livingstone and Edinburgh Airport chairman Sir John Elvidge.
The royal couple were then driven from the airport, escorted by police.
The King is due to inspect a guard of honour at the Palace of Holyroodhouse before attending a Ceremony of the Keys on the forecourt.
5. King Charles III and the Queen Consort inspect the Guard of Honour before the Ceremony of the Keys
King Charles III and the Queen Consort inspect the Guard of Honour before the Ceremony of the Keys at the Palace of Holyroodhouse, Edinburgh. Picture date: Monday September 12, 2022. Photo: Peter Byrne
6. King Charles III and the Queen Consort arrive at Edinburgh Airport
King Charles III and the Queen Consort arrive at Edinburgh Airport after travelling from London, ahead of joining the procession of Queen Elizabeth's coffin from the Palace of Holyroodhouse to St Giles' Cathedral, Edinburgh. Picture date: Monday September 12, 2022. Photo: Robert Perry
7. King Charles III and the Queen Consort arrive at Edinburgh Airport after travelling from London
King Charles III and the Queen Consort arrive at Edinburgh Airport after travelling from London, ahead of joining the procession of Queen Elizabeth's coffin from the Palace of Holyroodhouse to St Giles' Cathedral, Edinburgh. Picture date: Monday September 12, 2022. Photo: Robert Perry
8. Scottish Secretary Alister Jack and First Minister of Scotland Nicola Sturgeon
Scottish Secretary Alister Jack and First Minister of Scotland Nicola Sturgeon leave Edinburgh Airport after the arrival of King Charles III and the Queen Consort, who will join other members of the royal family for the procession of Queen Elizabeth's coffin from the Palace of Holyroodhouse to St Giles' Cathedral, Edinburgh. Picture date: Monday September 12, 2022. Photo: Owen Humphreys