Zuma said the burial will be preceded by a national day of prayer and reflection Dec. 8, and then a memorial service Dec. 10 in a Johannesburg stadium. Mandela's last public appearance was at the same stadium in 2010 for the closing ceremony of the soccer World Cup.
The anti-apartheid leader died Thursday at the age of 95 after battling a prolonged illness. His body was taken by military escort to Pretoria, where it will lie in state at government buildings for three days.
"We've lost our greatest son," Zuma said upon announcing Mandela's death to the world.
South Africans erupted in song, dance and tears in public and emotional celebrations of Mandela's life, the man who bridged the country's black-white divide and helped avert a race war. Many wore traditional garb of Zulu, Xhosa and South Africa's other ethnic groups. One carried a sign saying: "He will rule the universe with God."
"What I liked most about Mandela was his forgiveness, his passion, his diversity, the impact of what he did," said Ariel Sobel, a white man who was born in 1993, a year before Mandela was elected president. "I am not worried about what will happen next. We will continue as a nation. We knew this was coming. We are prepared."
At a peace and security summit in Paris, a moment of silence was observed for Mandela. South African Foreign Minister Maite Mashabane told the summit that Africans must work together to achieve peace and fulfill Mandela's vision.
"We will do so if we work together to find a peaceful resolution so that our people can continue to put peace, security and development together in the name of our father, who chose no revenge, who said South Africa belongs to all living in it, irrespective of color or creed, who made the impossible possible," Mashabane said.
Mandela's final campaign was against AIDS in South Africa. Six years after retiring from a political career, Mandela called a news conference in January 2005 at his home in Johannesburg, South Africa, to make the stunning announcement that his son died of AIDS at the age of 54. Two other family members of Mandela's later died of complications from the disease.
"We must not hide the cause of death of our respected family because that is the only way in which we can make people understand that even HIV is an ordinary illness," Mandela said.
Mandela created the 46664 charity, named for his old prison number, 466, and 1964, the year he was jailed, which is now used to raise awareness and money in the fight against AIDS.
ABC News and The Associated Press contributed to this report.