Small, who died in Cape Town on Wednesday, was praised for his performance in the World Cup final, where his fearless tackles on giant New Zealand winger Jonah Lomu helped the Boks to a surprise victory at Ellis Park.
Small was rushed to hospital in Johannesburg on Tuesday night, and died on Wednesday.
The 50-year-old Small, who had been visiting Cape Town, lived with his daughter Ruby in Johannesburg and was on his way back home.
Mark Alexander, the president of SA Rugby, has shared his condolences with Small's family and friends.
Brett Gosper, CEO of World Rugby, said: Very sad to hear the news of former Springbok James Small - the man who, among other achievements, marked Jonah Lomu during South Africa's victorious and iconic 1995 Rugby World Cup Final.
He scored 20 tries, the last of which at the time broke South Africa's Test record previously set by Danie Gerber.
Known for his aggressive style of play, Small was the first South African to be sent off in a Test after being shown a red card against Australia in 1993.
Tributes have flooded in for Small since news emerged of his passing. "You know you can't play it".
Small is the fourth member of the Springbok squad from 1995 to pass away, after Kitch Christie (coach), Ruben Kruger (flank) and Joost van der Westhuizen (scrumhalf). Our deepest sympathies go out to the family, friends and the Springboks'.