Blatter hailed Mandela'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 in a statement: "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.
"As a mark of respect and mourning, the flags of the 209 member associations at the home of FIFA will be flown at half-mast and there will be a minute's silence before the next round of international matches."
Everton midfielder Steven Pienaar, who represented South Africa at the 2010 World Cup, said on Twitter: "God Bless the MADIBA family. Still can't believe it MADIBA is gone."
Mandela unforgettably presented South Africa's rugby union captain Francois Pienaar with the World Cup in 1995 at Ellis Park, Johannesburg.
The image of Mandela, dressed in a Springbok rugby shirt and cap, handing over the Webb Ellis trophy has become one of the most iconic and evocative images in the history of sport.
Joost van der Westhuizen, who played in the 1995 World Cup final, said on Twitter: "A sad day for our country. Rest in Peace Madiba. Condolences to his family and friends."
Current South Africa international Bryan Habana wrote: "Thank you for the inspiration and hope. May your legacy live on forever. #forevergrateful #proudlySouthAfrican."
Tributes poured in from sportsmen and sporting organisations across the world.
Cricket South Africa said on their official Twitter account: "RIP Tata Mandela. It is because of you that a represented Proteas team can express their talent across the globe #mandela."
Usain Bolt said: "One of the greatest human beings ever..May your soul rest in peace..The worlds greatest fighter..."
South Africa's one-day international cricket captain AB de Villiers saluted the legacy of Mandela, tweeting: "Let us now, more than ever, stick together as a nation! We owe him that much. #madiba you will be missed! #tata #inspiration #leader."
England and Australia Cricket confirmed both teams would wear black armbands and observe a minute's silence ahead of the second day of the second Ashes Test.
South Africa Rugby said on Twitter: "Rest in Peace Nelson Mandela. We will never forget the role you played in our country, in our sport, and for that we are eternally grateful."
Cristiano Ronaldo offered his tribute, saying: "Thankful Madiba for your legacy and your example. You"ll always stay with us."
Rafael Nadal said: "Rest in peace Nelson Mandela, you have been a role model to the world. My most sincere condolences to family and friends."