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.
1. King Charles III and the Queen Consort (left) are greeted by First Minister Nicola Sturgeon as they arrive at Edinburgh Airport
King Charles III and the Queen Consort (left) are greeted by First Minister Nicola Sturgeon as they 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
2. King Charles III arrives at Edinburgh Airport
King Charles III arrives at Edinburgh Airport after travelling from London with the Queen Consort, ahead of joining the procession of Queen Elizabeth's coffin from the Palace of Holyroodhouse to St Giles' Cathedral, Edinburgh. Photo: Owen Humphreys
3. First Minister Nicola Sturgeon after greeting King Charles III and the Queen Consort
First Minister Nicola Sturgeon after greeting King Charles III and the Queen Consort as they arrived 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
4. King Charles III and the Queen Consort are driven along the Royal Mile
King Charles III and the Queen Consort are driven along the Royal Mile ahead of the Procession of Queen Elizabeth's coffin from the Palace of Holyroodhouse to St Giles' Cathedral, Edinburgh. Picture date: Monday September 12, 2022. Photo: Jon Super