In his application for leave to appeal, the President had contended that there was a reasonable prospect that another Court would come to a different decision from that of the High Court and that the matter was one of considerable importance to the parties and the country.
In a statement the Presidency said: "The application for leave to appeal was argued today, June 2, 2017, before Judge Vally and he agreed that the President be granted leave to appeal his judgment to the Supreme Court of the Appeal.
"In handing down judgment, the court emphasised that the public interest in this case post issuance of the judgement has been wide, deep and intense and warranted that the the issues raised by this particular matter be considered by the Supreme Court of Appeal.
"Further, the court agreed that there is merit in the contention by the President that the order had far-reaching implications and therefore warranted the attention of a higher court."
Zuma may now approach the Supreme Court of Appeal. Earlier on Friday, the South Gauteng High Court granted Zuma leave to appeal but Judge Vally said he remained sceptical and believed there were no reasonable prospects that another court would come to a different conclusion.
However, he conceded that there might compelling reasons to appeal.
"The president's contention is not without merit. The president contends further that the order fundamentally impacts on the manner in which the office of the Presidency operates. The DA was not able to dispel or discredit these claims. In these circumstances this matter should be brought to the attention of a higher court."
Last month, the Democratic Alliance approached the court to compel Zuma to hand over all records which supported his reasons for sacking former Finance Minister Pravin Gordhan and his deputy Mcebisi Jonas during a midnight reshuffle in March.
In his first ruling, Vally ordered Zuma to provide all documents and electronic records, including correspondence, reports, contracts, memoranda, evaluations, advice received and recommendations that related to his decision.
Zuma has continuously maintained that he is empowered through the constitution to hire and fire members of his cabinet and that the decision to axe Gordhan and Jonas was an executive one.