The South African-born D'Oliveira died while fighting Parkinson's disease, leaving a legacy for his role in the opposition to the apartheid system in his native land.
"He was a man of true dignity and a wonderful role model as somebody who overcame the most extreme prejudices and circumstances to take his rightful place on the world stage," Gerald Majola, the chief executive of Cricket South Africa, said in a written statement.
D'Oliveira could have been a star for the South African national team; however, he was of mixed race and therefore barred from playing on the all-white squad.
Britain's The Daily Telegraph said D'Oliveira eventually moved to England in the 1960s. He was selected to the British national team but was barred from taking part in a tour of South Africa in 1968.
The situation resulted in Britain's boycott of the tour, which intensified the international spotlight on apartheid. As a result, no official team from any nation toured South Africa until the race-based system was abolished in 1990.
"Throughout this shameful period in South Africa's sporting history, Basil displayed a human dignity that earned him worldwide respect and admiration," said Majola.
Aside from his contribution to history, D'Oliveira did his fair share on the cricket field. He played in 44 test matches, scoring 2,484 runs, with five test centuries and a batting average of 40.06, the Daily Telegraph said.