Following consultations with the Chairmen of the regional groups of member states, Mr Ban informed the General Assembly of his intention to appoint Prince Zeid Ra'ad Zeid Al-Hussein as the chief of the human rights body.
Mr Al-Hussein, 50, graduated from Johns Hopkins University and received a Ph.D. from the University of Cambridge. He is currently Jordan's Permanent Representative to the United Nations, a post he held previously for six and a half years, from 2000 to 2007.
From 2007 to 2010 he served as Jordan's Ambassador to the United States and non-resident Ambassador to Mexico. He has also served as Jordan's Deputy Permanent Representative at the UN, with the rank of Ambassador, from 1996 to 2000.
Mr Al-Hussein will replace Ms Pillay, who was appointed High Commissioner for Human Rights in July 2008 and her mandate was renewed for two years beginning September 2012.
A South African national, Ms Pillay was the first woman to start a law practice in her home province of Natal in 1967.
In 1995, after the end of apartheid, Ms Pillay was appointed as acting judge on the South African High Court and in the same year she was elected by the UN General Assembly to be a judge on the International Criminal Tribunal for Rwanda, where she served a total of eight years.
In South Africa, as a member of the Women's National Coalition, she contributed to the inclusion of the equality clause in the country's Constitution that prohibits discrimination on grounds of race, gender, religion and sexual orientation.
Ms Pillay, who holds a Master of Law and a Doctorate of Juridical Science from Harvard University, co-founded Equality Now, an international women's rights organisation.
She has been involved with other organisations working on issues relating to children, detainees, victims of torture and of domestic violence and a range of economic, social and cultural rights.