A high court judge dismissed the charges of corruption, fraud, money laundering and racketeering last year.
But the appeals court overturned that decision in January.
Zuma's lawyers provided prosecutors with recordings of Bulelani Ngcuka, the former head of the NPA, and Leonard McCarthy, the former chief of the elite Scorpions investigative unit, conspiring over how to gain political mileage from the case, Mokotedi Mpshe, the current NPA head, said.
The decision to drop the charges was not based on the quality of the prosecution's case against Zuma, but because McCarthy's conduct had tainted the legal process, he said.
"It is not so much prosecution itself that is tainted, but the legal process that is tainted"
National Prosecution Authority head
"Mr McCarthy used the legal process for a purpose outside and extraneous to the prosecution itself," he said.
"It is not so much the prosecution itself that is tainted, but the legal process that is tainted."
Hundreds of Zuma's supporters celebrated in Johannesburg after the announcement.
"I'm very happy for the decision, hoping that this gives our president what he needs for us to go forward," Victress Iwabi, an ANC town councillor, said.
Earlier, about 20 supporters of the Congress of the People (Cope), which broke away from the ANC last year, had gathered outside the national prosecutors' office demanding that Zuma face trial.
"Comrade JZ must face his day in court. He has been tried in a secret office but the public deserves to know the merits of the case," Mgcini Tshwaku, the Cope youth secretary, said.
Zuma was deputy president for six years before he was sacked in 2005 by Thabo Mbeki, the former South African president, after being implicated in a trial that saw his former financial adviser convicted of fraud and corruption charges.
In May 2006, Zuma was acquitted of rape charges.
Adam Habib, a political analyst and vice-chancellor of the University of Johannesburg, said the court's decision to drop the charges did not prove that Zuma was innocent of corruption.
"If Zuma is interested in the integrity of his political administration, then he has to do something more," Habib said.
"He has to take the nation into his confidence, call a press conference and say exactly what has happened. If he does not do that, then his political administration will be compromised and the country will suffer irreparable damage."
A poll released on Friday suggested that the ANC would secure more than 64 per cent of the vote in the election, just short of the two-thirds majority that it currently holds, which allows the party to push through constitutional amendments.