Zuma was speaking here this evening after the Independent Electoral Commission announced the final results of the national elections held on Wednesday that saw the African National Congress (ANC) led by Zuma win overwhelming majorities in all but one of the nine provinces of South Africa and 249 of the 400 seats in the national assembly.
Zuma will return as president for a second term.
"We dedicate our victory to Madiba's memory and pledge to continue taking forward his legacy and that of his peers and forebears working with all our people," Zuma said as he reminded the audience that he was speaking on the day that Nelson Mandela took the oath of office 20 years earlier as South Africa's first democratically elected president after decades of white-minority apartheid rule.
New party Economic Freedom Fighters (EFF) won 25 seats in the national assembly.
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"This election victory has reconfirmed just how deeply rooted the ANC is in the hearts and minds of the overwhelming majority of South Africans," Zuma said.
"It is an affirmation of our assertion that South Africa has a good story to tell and we have made this country a much better place to live in than it was before 1994," he said.
Zuma promised to use the ANC majority to implement policies and programmes to address the lack of service delivery which has seen huge protests in many areas in the run-up to the elections.