A fertiliser tycoon, Luyt was at the helm of South Africa rugby when it returned from isolation in the early 1990s and stood alongside Mandela on the podium when South Africa won the 1995 World Cup in Johannesburg.
But he clashed with the South African president three years later over a government-ordered enquiry into allegations of lingering racism in rugby and took Mandela to court to back his refusal to appear.
The Golden Lions Rugby Union, known as Transvaal when Luyt was president, said in a statement on Friday Luyt was able to play a critical role in the re-entry of the Springboks to international competition, following more than a decade of isolation.
Luyt, who was a lock in his playing days and a towering figure in his business and sports administration career, caused a walkout at the official dinner after the 1995 World Cup final win over New Zealand when he suggested South Africa would have won the first two tournaments they were not allowed to play in.
He then tried to give a gold watch to referee Derek Bevan because South Africa had escaped with a narrow semi-final win over France when the Welshman failed to award the French a genuine-looking try.
Luyt left rugby in 1998 to form a political party and briefly owned a Soweto-based soccer club, Moroka Swallows.