South African foreign affairs spokesman Ronnie Mamoepa said the family had requested the repatriation for a funeral service and cremation.
Makeba - known as Mama Africa - spent 31 years in exile during apartheid.
Paying tribute to her, South African ex-President Nelson Mandela said she was the "mother of our struggle" and "South Africa's first lady of song".
A date has not yet been set for the funeral service.
Mr Mandela said her haunting melodies gave voice to the pain of exile.
"She... richly deserved the title of Mama Africa," Mr Mandela said in a message.
Songs banned
South Africa's governing African National Congress (ANC) also paid homage to her musical contribution "to the liberation of South Africa".
"One of the greatest songstresses of our time has ceased to sing," South African Foreign Affairs Minister Nkosazana Dlamini Zuma said.
Makeba was born in Johannesburg on 4 March 1932. Her singing career started in the 1950s as she mixed jazz with traditional songs.
She was forced into exile soon after when her passport was revoked after starring in an anti-apartheid documentary and did not return to her native country until after Mr Mandela was released from prison in 1990.
In 1963, Makeba appeared before the UN Special Committee on Apartheid to call for an international boycott of South Africa.
It was while living in exile in the US that she released her most famous songs, Pata Pata and the Click Song, which were banned at home.
Makeba was the first black African woman to win a Grammy Award, which she shared with Harry Belafonte in 1965.
Charlie Gillett, who presents the BBC World of Music programme, says there is nobody to compare to her, as she was popular in West Africa - after living in exile in Guinea - and East Africa - she recorded a version of the Swahili song Malaika, as well as her home in South Africa.
She was African music's first world star blending different styles long before the phrase "world music" was coined.
After her divorce from fellow South African musician Hugh Masekela, she married American Black Panther Stokely Carmichael and moved to Guinea.
"You sing about those things that surround you," she said. "Our surrounding has always been that of suffering from apartheid and the racism that exists in our country. So our music has to be affected by all that."
Makeba announced her retirement three years ago, but despite a series of farewell concerts she never stopped performing.
When she turned 75 last year, she said she would sing for as long as possible.
BBC
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