Pillay, 67, who said she wants to be the "the champion of human rights in every part of the world," will take up her new post on September 1, replacing Louise Arbour, a former Canadian Supreme Court judge. Her term is for five years.
Born in the South African city of Durban, Harvard-educated Pillay, who is of Tamil descent, became the first woman to establish a legal practice in South Africa's Natal province.
Pillay has served as judge on the International Criminal Court at The Hague since 2003. She was also president of the UN tribunal for Rwanda genocide hearings.
Secretary-General Ban Ki-moon, who nominated Pillay to the post last week, said that he was "gratified" by the General Assembly's approval, adding that human rights should remain high on the UN agenda.
The 47-nation UN Human Rights Council, based in Geneva, was established in 2006 over U.S. opposition to replace a previous commission that had been criticized for its poor human rights record.
