The bombshell charges earlier this month had driven a wedge between rival camps in the ruling African National Congress, rattled the markets and led to a fall in the value of the rand.
"I have directed the summons to be withdrawn with immediate effect," Shaun Abrahams told journalists, saying the charges against him would be difficult to prove.
The move came a day after Abrahams' spokesman had rubbished a report saying the prosecutor had decided to drop the charges, describing it as "absolute hogwash".
Announcing the decision, Abrahams said he did not believe Gordhan intended to break the law.
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"I foresee difficulties to prove knowledge of unlawfulness," he said.
Gordhan has claimed the charges were politically motivated, and won backing from several high-profile ANC politicians, the nation's deputy president Cyril Ramaphosa, numerous ministers and scores of business leaders.
His imminent prosecution had sparked investor fears that he would also be sacked, as the country reels from an economic downturn and declining business confidence.
"There will be a perception that the prosecuting authority is being used as a football in a game of state capture," said February, an analyst with the Pretoria-based Institute for Security Studies.
Gordhan has been a vocal opponent of corruption and excessive spending by President Jacob Zuma's government, which has been hit by a series of graft scandals and slowing economic growth.
Abrahams rejected claims that the charges against Gordhan were politically motivated, saying he did not "pay regard to political considerations."
Last week, the ANC's chief whip Jackson Mthembu lambasted Gordhan's prosecution, saying the decision to use state institutions to fight political matters should force the entire ANC leadership to resign.