The anti-apartheid hero will lie in state in the capital Pretoria.
Thousands of people lined the streets as a procession of police motorcycles lead the black hearse carrying Mandela's coffin, draped in the South African flag.
Mandela's death last Thursday at the age of 95 has sparked an outpouring of grief and mourning in the country he led from 1994 to 1999 as its first black president.
"This is a significant moment for me and my children," said 48-year-old teacher Thapelo Dlamini, who had been waiting on the street for two hours with his two children.
Mandela's body will lie in state for three days at the Union Buildings, where he was inaugurated as president in 1994 after the first all-race elections that ended decades of white-minority apartheid rule.
Traffic in Pretoria was gridlocked from early in the morning, and shops along the procession route were closed.
The road closures and snarled traffic were a disruption for some Pretoria residents.
"I am trying to pass through to get to work," said one woman. "I respect Mandela but the mourning has gone on for way too long. I don't think he would have liked this."
Mandela will be buried on Sunday in Qunu, his ancestral home in the rolling hills of the Eastern Cape province, 700 km (450 miles) south of Johannesburg.