Mandela's death at his home on Thursday aged 95 sparked a wave of emotional tributes from sportsmen from South Africa and across the world.
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. He was 95 and led a full life but a lot of that wasn't spent on what he was so good at because he was away for so many years.
"I met him for the first time in 1994 with Mr (Johann) Rupert when we had a dinner together and then after that we stayed in touch. I used to play that tournament at Houghton and his home was very close to Houghton Golf Club. He came over one time and we exchanged gifts with each other. I have still got the picture from that day in 1996 in my office in the US. And then every time I won a tournament he used to call me.
"He was our president and the man who changed our lives. It could have been so different in South Africa but he kept his head and kept everyone going forward. I was in the Air Force when the ANC (African National Congress) was banned. I remember those days in the 1980s when the government was against the ANC. You know, they were our enemies.
"And then President Mandela comes in and takes over the country and leads it in a democratic way. He was an unbelievable guy and the guys who lived in that generation will really miss him."
World number one Tiger Woods wrote 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..."
Mandela, who created one of rugby union's iconic images at the 1995 World Cup, has been hailed for his ability to use sport to unite and inspire.
The image of Mandela, dressed in a Springbok rugby shirt and cap, handing over the Webb Ellis trophy to South Africa captain Francois Pienaar at Ellis Park in Johannesburg has become one of the most iconic and evocative images in the history of sport.
South African Rugby Union chief Oregan Hoskins said in a statement: "Madiba was a true icon of inspiration and as much as South Africa owes so much to him, so does rugby.
"Through his extraordinary vision, he was able to use the 1995 Rugby World Cup as an instrument to help promote nation building just one year after South Africa's historic first democratic election."
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."
Cricket South Africa president Chris Nenzani dedicated the Proteas' ongoing series against India to Mandela and captain Graeme Smith said: "Madiba was an inspiration to the Proteas in the same way that he was to other South African teams.
"To us he represented so many of the qualities which we as players have looked to adopt in playing for South Africa. As the captain I was very privileged to spend some time with him and I vividly recall telephone calls I received from him wishing us luck before a big match or event.
"He always gave simple but wise advice and this had a big impact on me as leader of the team. His words will stay with me forever as they were not only relevant to cricket, but also to life.".
FIFA president Sepp Blatter paid an emotional tribute to his "dear friend'', hailing the 95-year-old's impact on the 2010 World Cup in South Africa.
He 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: Nelson Rolihlahla Mandela.
"He and I shared an unwavering belief in the extraordinary power of football to unite people in peace and friendship, and to teach basic social and educational values as a school of life.
"When he was honoured and cheered by the crowd at Johannesburg's Soccer City stadium on 11 July 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'.
"Nelson Mandela will stay in our hearts forever. The memories of his remarkable fight against oppression, his incredible charisma and his positive values will live on in us and with us."