The top diplomat, currently Amman's ambassador to the United Nations, will take over as UN high commissioner for human rights on September 1, replacing Navi Pillay of South Africa.
UN Secretary General Ban Ki-moon nominated Zeid, who holds a PhD from Cambridge University, for a four-year mandate last week.
Widely respected, Zeid is steeped in peacekeeping and international justice and played a key role in the establishment of the International Criminal Court.
For more than two years, he chaired complex negotiations on the elements of individual offenses for the crimes of genocide, crimes against humanity and war crimes.
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In a first reaction, Zeid told the General Assembly he was "very honored by the confidence" instilled in him, noting he will be the first high commissioner from the Asian continent, as well as the Arab and Muslim world.
"This reflects the willingness of the international community to advance this matter on this continent as well as in other parts of the world, taking into account the independence and the mandate of the high commissioner," he added in a brief address in Arabic.
Zeid currently represents Jordan on the UN Security Council, where Amman has a two-year term. He was also his country's ambassador to the United States and Mexico.
Zeid is married and has three children.