Zuma had sought to overturn a court order in April that the National Prosecuting Authority (NPA) should reinstate the charges that were dropped in 2009.
The president has battled several corruption scandals while in office, as well as enduring growing criticism focused on South Africa's record unemployment and poor growth rate.
"We seriously considered whether the appeal would have reasonable prospects of success and came to the conclusion that there are no merits in the arguments," Judge Aubrey Ledwaba told the High Court in Pretoria.
In 2009, state prosecutors justified dropping the 783 charges by saying that tapped phone calls between officials in then-president Thabo Mbeki's administration showed undue interference in the case.
The move cleared the way for Zuma to be elected president just weeks later.
Pressure on the president would increase if some or all of the charges -- which relate to alleged corruption, racketeering, fraud and money laundering over a multi-billion dollar arms deal -- were reinstated.
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