Mandela's appearance in a Springboks shirt and baseball cap to present the 1995 Rugby World Cup trophy to Pienaar has been seen as a defining moment in transforming South Africa into a multi-racial democracy.
It inspired the Hollywood film Invictus, and Pienaar told Sky Sports News: "The enormity of his impact is very difficult for me to describe.
"The impact he had on me as an individual - I've been very blessed, I was at the right place at the right time, more so than any Rugby World Cup captain before me and after me.
"What he did for the team was wonderful to watch - that air of confidence that he brought with him and that unbelievable humility that 'Madiba' had is something that rubbed off - and I never thought he would wear a Springbok jersey!"
Current Springboks star Bryan Habana added on Twitter: "R.I.P Tata Madiba. Thank you for the inspiration and hope. May your legacy live on forever."
South African golfer Ernie Els hailed the former South African president as an "iconic leader".
Els met Mandela several times and was among the players who wore black ribbons and observed a minute's silence before play resumed in the Nedbank Golf Challenge in Sun City on Friday.
"It is a very sad day, a very sad day for South Africa and the world," Els said.
"We have lost one of the iconic leaders of our time. You cannot say anything bad about the man.
"He fought for what he believed in, went to prison for so many years and came out to lead our country up until now. He was the father of our country and our continent."
Tiger Woods said on Twitter: "You will always be in my heart Mr. Mandela. Pop & I felt your aura when we met, I feel it today & I will feel it forever. You have done so much for humanity..."
In Australia, the hosts and England wore black armbands and observed a minute's silence ahead of the second day of the second Ashes Test.
Giles Clarke, the England and Wales Cricket Board chairman, said: "Nelson Mandela was a truly inspirational statesman for many generations of South Africans as well as many people around the world. Under his patronage South African sports, including cricket, emerged from the dark shadow of apartheid."
FIFA president Sepp Blatter hailed Mandela's impact on the 2010 World Cup in South Africa and said there would be a minute's silence as a mark of respect ahead of the next round of international matches.
Blatter said: "It is in deep mourning that I pay my respects to an extraordinary person, probably one of the greatest humanists of our time and a dear friend of mine.
"When he was honoured and cheered by the crowd at Johannesburg's Soccer City stadium on July 11, 2010, it was as a man of the people, a man of their hearts, and it was one of the most moving moments I have ever experienced. For him, the World Cup in South Africa truly was 'a dream come true'."
Other legendary sporting names also added their own tributes.
Pele, Brazil's football great, said: "He was my hero, my friend, and also a companion to me in our fight for the people and for world peace."
South African golfer Gary Player tweeted: "Nelson Mandela's courage, forgiveness, love & hope inspired people around the world. He made me want to be a better man. RIP Tata."
Boxing was Mandela's favourite sport as a young man, and three-times world heavyweight champion Muhammad Ali paid a special tribute on his website.
He said: "What I will remember most about Mr Mandela is that he was a man whose heart, soul and spirit could not be contained or restrained by racial and economic injustices, metal bars or the burden of hate and revenge."
Jamaica's Usain Bolt, the world's fastest man, said on Twitter: "One of the greatest human beings ever. May your soul rest in peace. The world's greatest fighter."
The Football Association added its tribute to Mandela - in 2003 a delegation of England players - including David Beckham, Michael Owen and Rio Ferdinand - went to meet him ahead of a match in Durban.
There will be a minute's applause to celebrate Mandela's life at all Premier League, Football League and FA Cup matches this weekend.
FA chairman Greg Dyke said: "He was one of the greatest men of any generation. Partly because of what he achieved but more so for his ability to forgive."
Former sports minister Richard Caborn, secretary of the Parliamentary anti-apartheid group during the 1980s, said Mandela had played an important part in securing the 2012 Olympics for London.
Caborn travelled to Johannesburg in 2005, three months before the International Olympic Committee vote, and secured his backing for London's bid.
Caborn told Press Association Sport: "I said to him 'Madiba, we are the only Commonwealth country bidding' and that was the key.
"He said he would love to support London and I think that was very important to the bid, and became part of the presentation at the vote in Singapore."
Caborn helped organise Mandela's first visit to Parliament in 1991, shortly after his release from prison, but due to opposition from ex-Prime Minister Margaret Thatcher and a group of right-wing Conservative MPs led by John Carlisle, no cameras were allowed to be present and Mandela had to enter via a side entrance.