The King was welcomed by a 21-gun salute outside parliament in Cape Town. Mr Mandela and the Swedish monarch exchanged medals and met privately for 40 minutes at the start of a three-day royal visit, which includes talks with Archbishop Desmond Tutu, who heads the post-apartheid Truth and Reconciliation Commission.
Mr Mandela, 78, last year confirmed his romance with Mrs Machel, 51, widow of the Mozambican president Samora Machel, and said they would try to spend two weeks a month together. The couple have appeared in public together in South Africa only twice before and never at a state function.
"This is the first time Mrs Machel has appeared with the President at a state function, but they will be appearing together a lot more in future," said an official in his office. The media programme for King Carl's three- day state visit had referred only to "President Mandela and his companion".
Reporters had expected the President to be accompanied as usual by one of his daughters. But as Mr Mandela led the King down the steps of his office for a chat with tourists and pedestrians at the gate, it was Mrs Machel who came down with Queen Silvia. Mr Mandela divorced his wife of 38 years, Winnie, 11 months ago.