"The Presidency accepts and respects the judgment of the Constitutional Court in relation to the unconstitutionality and invalidity of Section 8(a) of the Judges' Remuneration and Conditions of Employment Act of 2001 and will abide by it," said Zuma's spokesperson Mac Maharaj.
"The law was valid until today's judgment, and government will now study the ruling to see what directives the Constitutional Court is giving to Parliament for remedial action."
Unanimous ruling
The Constitutional Court on Friday unanimously ruled that it was unconstitutional for Zuma to extend Ngcobo's term of office.
Section 176(1) of the Constitution says that a judge holds office for a non-renewable term of 12 years or until he or she reaches the age of 70 - whichever comes first - except where an act of Parliament extends the term of office of a Constitutional Court judge.
The court declared Section 8a of the Judges Remuneration and Conditions of Employment Act - in terms of which Zuma extended Ngcobo's term -unconstitutional.
It found that the section allowed the president to "usurp" the power of Parliament and held that Parliament alone had the power to extend a Constitutional Court judge's term of office.
Zuma and the Justice Minister were ordered to pay costs.
It was announced on Wednesday that Ngcobo had decided to withdraw his acceptance of Zuma's extension, which left the post of chief justice open from August 15 should a replacement not be found by then.
The application against the way Zuma offered Ngcobo an extended term was brought by the Council for the Advancement of the SA Constitution, Freedom under Law, the Justice Alliance of SA and the Centre for Applied Legal Studies.
Maharaj said Zuma had begun the process of identifying a new chief justice and it would be done "in accordance with the provisions outlined in the Constitution of the Republic".
Constitutional democracy
ANC chief whip Mathole Motshekga, speaking after the judgment was handed down, said the current Parliament was the fourth since 1994, and found laws in place which the executive had to implement.
"There is nothing that the president should be embarrassed about, and nothing that Parliament should be embarrassed about.
"In a Constitutional democracy there will be laws that are found to be unconstitutional, that's why we have a Constitutional Court, that's what makes our democracy vibrant... we are happy about that."
Centre for Legal Studies director Raylene Keightley said she was "delighted" with the outcome.
She said the reaction from the ANC "put the best spin possible" to "regaining the integrity of the president". She said the unconstitutionality of section 8(a) was "fairly clear" and found it "worrisome" that the President had legal advice leading up to the litigation and did not pick up on this.
She was not surprised by the judgment.