Mandela emerged from 27 years in prison under the white racist government in 1990, appealed for forgiveness and reconciliation and became president in 1994 after the country's first all-race democratic elections.
People lined the streets to watch the procession drive slowly to the Union Buildings.
They sang old songs from the struggle against the apartheid regime and called out their farewells to Mandela, who died Dec. 5 at the age of 95.
Traffic was backed up for several kilometers (miles) on a highway leading into Pretoria.
President Jacob Zuma named the amphitheater after Mandela by decree on Tuesday.
The Union Buildings, described by the South African government as a “modern-day acropolis,” sit atop a hill overlooking Pretoria.
The architect who designed it envisioned its two wings, made of half a million cubic feet (14,100 cubic meters) of stone, representing the Afrikaans and English languages spoken in the country—but none of the land's native languages.
Even from its inception, the building long has been considered a symbol of governance in the country—and of apartheid until Mandela took office.
Mandela's grandson Mandla and Defense Minister Nosiviwe Mapisa-Nqakula led mourners into the viewing area. After casket bearers left, four junior officers in white uniform from the South African navy remained to keep watch over the body, rotating position every hour.
Mandela's body will lie in state for three days.
It has a glass cover allowing mourners to look in on Mandela one last time.
Officials have banned cameras from the viewing area and people are being asked to turn off their mobile phones.
