Some onlookers had been waiting at the airport for almost 10 hours before the team appeared.
In the arrivals area, coach Jake White and captain John Smit lifted the Webb Ellis trophy together as they were cheered on by an elated crowd.
There was also a particularly loud cheer for winger Bryan Habana, who was named the International Rugby Board's player of the year.
Smit admitted that he was "overwhelmed" by the reception, describing the turnout as "far beyond what we ever imagined".
White added: "You can be the best coach in the world - but if you don't have a good captain you cannot be a good coach."
The country's deputy sport minister Gert Oosthuizen said: "You not only united us - you filled us with pride and made us winners.
"Let's take this positive momentum forward and build and do not forget that 2011 (South Africa host the World Cup) is around the corner."
Shortly after the press conference, the team broke up and headed their separate ways to spend time with their families.
They will regroup in Johannesburg on Friday for a series of parades and public appearances across the country including Pretoria, Bloemfontein, Port Elizabeth and Durban, before finishing off in Cape Town on Monday where they will hand over the trophy to SA Rugby chief executive officer Jonathan Stones.