Chaudhry will assume office on March 22 after the retirement of incumbent Abdul Hamid Dogar.
Chaudhry's reinstatement would take effect from March 22 consequent to the retirement of Dogar, said a brief statement issued by presidential spokesman Farhatullah Babar.
Babar also said the president had reinstated other deposed judges of the Pakistan supreme court and provincial high courts with immediate effect. He gave no other details.
Zardari's ruling PPP on Monday buckled under pressure from the lawyers' movement and
opposition Pakistan Muslim League-Nawaz for reinstating judges deposed by former president Pervez Musharraf during the 2007 emergency rule.
Prime Minister Yousuf Raza Gilani announced the government's decision to reinstate the judges as PML-N chief Nawaz Sharif was leading thousands of supporters in a long march to Islamabad to pressurise the government on the issue.
Sharif subsequently called off the protest after it was announced that the judges would be reinstated.