The 95-year-old liberation hero died at a hospital in Singapore on Friday.
Mugabe served as prime minister of Zimbabwe from 1980 to 1987 and then as president from 1987 to 2017.
Parliament issued a statement on Friday, mourning Mugabe’s passing.
“He is one of the leading Statesmen in the African Continent whose pivotal contribution to the liberation of the African masses will never be forgotten. Parliament of the Republic of South Africa conveys its heartfelt condolences to family, friends and the entire Zimbabwean population,” the statement said.
In a statement from the Thabo Mbeki Foundation, former South African president Thabo Mbeki said he had kept in contact with Mugabe while he was undergoing treatment in Singapore.
Mugabe will be remembered as “outstanding fighter for the liberation not only of the people of Zimbabwe but also all other colonially and racially oppressed peoples”, Mbeki said.
“Having begun his involvement in that struggle as a member of the ANC Youth League at Fort Hare, he grew to become an important member of the group of Frontline States in Southern Africa which made a sterling contribution to our own struggle for emancipation from apartheid,” Mbeki said.
“Zimbabwe has lost a father of the nation! As Africans, we have lost an eminent leader of our victorious struggle for national liberation!”
On Friday, President Cyril Ramaphosa expressed his condolences to Zimbabweans on behalf of South Africa, following the news of the Mugabe’s death.
The president said under Mugabe’s leadership, Zimbabwe sustained a “valiant” struggle against colonialism, inspiring South Africa’s own efforts in its own battle against an apartheid regime.
The Department of International Relations and Cooperation (Dirco) has also extended its condolences to the government and the people of Zimbabwe following Mugabe’s passing.
Minister Naledi Pandor said: “South Africa expresses her sympathies to the people and government of Zimbabwe, president Mugabe was a great freedom fighter who played a sterling role in the freedom of Africa as well as in leading the struggle and building democracy in Zimbabwe.”