Boraine was co-founder of the Truth and Reconciliation Commission (TRC) and its vice-chairperson.
The 87-year-old passed away at home in his sleep on Tuesday morning.
“As deputy chairperson of the TRC, Alex was measured, reassuring, organised and efficient," Tutu said.
"He made sure things ran in the appropriate order and on time. He was more than a right-hand man.
"I could not have managed the commission without him,” he said.
Boraine was ordained as a Methodist minister in 1956.
He studied at Rhodes University in the Eastern Cape, Oxford University in England and Drew University in the US.
In 1970, he was appointed the youngest president of the Methodist Church of Southern Africa, a position he held until 1972.
He was elected to Parliament as an MP for the Progressive Party in 1974.
In 2001, Boraine co-founded the International Centre for Transitional Justice (ICTJ), an international human rights NGO, where he served as the president for three years and was subsequently chairperson of ICTJ’s South Africa office.
“We send our deepest condolences to the family as we thank God for Alex, a fellow traveller in the journey for a better South Africa.
"May he rest in peace and rise in glory,” Tutu said.@MarvinCharles17