Prince Zeid was appointed for a four-year term as human rights chief beginning September 1 after the mandate that Pillay, who served a four-year term and a consecutive two-year extension, is ending in August.
Prince Zeid will be the first representative from an Arab country or the continent of Asia to hold the position.
"I thank you all for the support and the trust you have shown this afternoon," Prince Zeid said. "I would like to express my high appreciation to Mrs Navi Pillay for her courageous endeavors, and Ihave the honour to be her successor."
DPA