Mandela died earlier this evening at the age of 95.
Mandela's body will be moved to a mortuary in Pretoria, and the state funeral is expected to take place next Saturday, December 14.
Zuma said all flags in South Africa will be lowered to half-mast and will remain like that until after Mandela is laid to res.
Mandela's death as it happened:
5.22 pm: Leading tributes, David Cameron said: "A great light has gone out in the world. Nelson Mandela was a hero of our time." The flag above Number 10 Downing Street is currently flying at half-mast as a mark of respect.
5.29 pm: US President Barack Obama said: "We will not likely see the likes of Nelson Mandela again. So it falls to us as best we can to forward the example that he set — to make decisions guided not by hate, but by love, to never discount the difference that one person can make, to strive for a future that is worthy of his sacrifice."
5.36 pm: The African National Congress (ANC) said South Africa had lost "a colossus, an epitome of humility, equality, justice, peace and hope of millions".
5.51 pm Labour leader Ed Miliband: "Nelson Mandela taught people across the globe the true meaning of courage, strength, hope and reconciliation.
"From campaigner to prisoner to President to global hero, Nelson Mandela will always be remembered for his dignity, integrity and his values of equality and justice."
5.57 pm: Prince William: "It is extremely sad and tragic news. We are reminded of what an extraordinary and inspiring man he was."