Thousands of people lined the streets as a procession of police motorcycles led the black hearse carrying Mandela's coffin, draped in the South African flag, from Military Hospital to the Union Buildings in the capital Pretoria.
Mandela's remains will lie in state for two more days, with thousands of people expected to pay their respects to him every hour, according to local media.
His 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 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.
Family members and world leaders viewed the body first. Leaders like Zimbabwe president Robert Mugabe, South African president Jacob Zuma and others passed by in two lines. Celebrities like singer Bono also paid their respects, as did FW de Klerk, the last president of white rule who shared a Nobel Peace Prize with Mr Mandela for ending the apartheid era.
Mandela's widow Graca Machel, his former wife Winnie Madikizela-Mandela and other family members also viewed his body.
Some appeared lost for a moment as they looked down at Mandela. South Sudan's Salva Kiir Mayardit stood transfixed before removing his trademark black cowboy hat and crossing himself.
By the afternoon the public had formed long queues but the government said the "cut-off" point had been reached, urging people instead to arrive early on the following two days.
Several people fainted in the stifling heat as they waited their turn to file past Mandela'scoffin.
In the UK, the Duke and Duchess of Cambridge formally paid their respects by signing his book of condolence at South Africa House in central London.
Mandela's body will be flown on Saturday to Qunu, his home in the Eastern Cape Province. He will be buried on Sunday.