Ms Pillay was the first non-white woman on South Africa's High Court
The US has welcomed the nomination of a South African judge as the next UN high commissioner for human rights.
Zalmay Khalilzad, US ambassador to the UN, said his country looked forward to working with Navanethem Pillay.
The US initially raised objections to the appointment, including Ms Pillay's support for abortion, diplomats said.
Ms Pillay has a background defending anti-apartheid activists in South Africa and is currently a judge at the International Criminal Court.
The UN General Assembly still has to approve Ms Pillay's appointment but is expected to do so on Monday.
Diplomats say UN Secretary General Ban Ki-moon has chosen someone in his own cautious image, the BBC's Laura Trevelyan reports from New York.
Human rights activists have questioned whether Ms Pillay would be sufficiently outspoken.
'Voice for human rights'
But Mr Khalilzad greeted the nomination.
"She has to be the voice for human rights, focus on the violations of human rights, speak clearly and focus world attention on the egregious violations of human rights that unfortunately still take place in many places around the world," he said.
"We look forward to working with her."
France and Britain also welcomed the appointment.
South Africa's UN ambassador Dumsani Kumalo dismissed concerns that she would be too close to the South African government, calling Ms Pillay "independent".
Ms Pillay, who is of Tamil descent, was born in 1941 and previously served as a judge on the UN war crimes tribunal for Rwanda.
In 1967 she became the first woman to start a law practice in Natal Province, and the first non-white woman to serve in the High Court in South Africa.
While practising in South Africa, Ms Pillay defended anti-apartheid activists and championed the rights of Nelson Mandela and other dissidents to legal assistance.
She would succeed Louise Arbour, who stepped down in March for personal reasons after four years in the post.
She faced fierce criticism from the governments whose human rights records she has questioned.