Perkins was born in Alice Springs. His father was an Aboriginal; sources differ about whether his mother was an Aboriginal or European.
When he was 10 he became one of the Stolen Generation (see Australian Aboriginal and Torres Strait Islander Children), sent to a boarding school in Adelaide. (He was actually taken with his mother's permission, but given under great pressure). (According to another source, he was raised at the Bungalow Mission in South Australia, where his mother was in charge of the girls' dormitory.)
He became one of the most influential Aboriginals in history: the first Aboriginal to graduate from a university (Sydney, 1966), and the highest-ranking Aboriginal civil servant (Secretary of the Department of Aboriginal Affairs, 1983). He received the Order of Australia in 1987, was named Aboriginal of the Year in 1993, and was awarded an honorary LLD by Sydney University in 2000. He was a founder of the Australian Aboriginal Cricket Association, a member of the Olympic Indigenous Advisory Board, president of the Arrernte Council of Central Australia, a consultant to the Australian Sports Commission, and deputy chairman of the Aboriginal and Torres Strait Islander Commission. He was outspoken in his criticism of racism in the Australian government and the paternalism of his own government department. In 1965 he led the Freedom Ride, similar to those in the US South, exposing rampant segregation in rural Australia. He was a passionate sportsman, and was rated one of the best soccer players in the country in his youth. He emigrated to the UK temporarily and played for Everton Football Club (Liverpool) in the 1950s.
He suffered from chronic kidney disease for many years, and had a transplant in 1972: on his death he was the longest surviving kidney transplant patient.