Rest in peace Joe...A true peoples champion.
"The world has lost a great champion," said 69-year-old Ali, who fought Frazier three times.
"I will always remember Joe with respect and admiration. My sympathy goes out to his family and loved ones."
Former heavyweight champion Lennox Lewis said of Frazier: "He was one of boxing's greats. He was legendary."
The Briton added: "He has made his mark in boxing, everyone knows his history.
"Without him, other boxing heroes wouldn't be great either because they really tested his talent against him.
"In a room filled of great men, he is definitely one of them."
Frazier, who won Olympic gold in 1964, became world champion in 1970 after Ali had been stripped of his titles in 1967 for refusing to fight in the Vietnam War.
When Ali tried to reclaim his belts, Frazier beat him, winning their much-hyped clash in 1971.
It was Ali's first loss as a professional, but a defeat he avenged.
Frazier and Ali met a further two times in the ring, Ali winning both contests, including the epic "Thrilla in Manila" in 1975.
The American also fought compatriot
George Foreman, another of boxing's heavyweight greats. They met twice, Foreman winning on both occasions.
Joe Frazier profile
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- Born 12 January 1944, Beaufort, South Carolina
- Total fights 37 - 32 wins (27KOs), 4 losses, 1 draw
- Won gold for USA at 1964 Tokyo Olympics
- Won NYSAC version of world title with victory over Buster Mathis in 1968
- Won WBA and WBC versions of world title with victory over Jimmy Ellis in 1970
- Last world title fight in 1975 against Muhammad Ali
- Retired in 1976 and made a comeback in 1981, fighting just once, before retiring for good
- Dies 7 November 2011 after suffering from liver cancer
Obituary: Joe Frazier
Foreman told BBC Radio 5 live: "Once I heard the news about Joe Frazier I found myself saying: 'Down goes George Foreman'.
"He was a wonderful man and a wonderful friend and the world won't be the same without him.
"Joe Frazier was the most amazing fighter. He never stood any more than 5ft 9in, some say 5ft 10in, but he was not that tall. Every big man in boxing was afraid of little guys.
"He was such a terror. Muhammad Ali and George Foreman were big guys but when we went in the ring with Joe Frazier, we had to have respect.
"I hoped I never had to fight him. He wouldn't back down. If you hit him, he liked it.
"The first thing I remember is when he missed [hitting] me. Just missing scared me so much that I knocked him down six times.
"Even when they stopped the boxing match to award me the championship of the world he was still on his feet.
"When Ali and Frazier fought, there will never be a spectacular moment in sport like that again. It was big."
Other boxing names, past and present, were also quick to pay their respects.
Joe Bugner, who lost to Frazier five months after being beaten by Ali in 1973, told BBC Radio 5 live: "Joe Frazier was relentless. Here was a man about 5ft 10in, he weighed about a stone lighter than myself, but he was so courageous and ferocious. You literally had to hit him with a sledgehammer to put him away.
Smokin' Joe one of the greats - Warren
"In 1973, I was 23 years old. I became a man after that fight because I realised you can't go through a career like boxing without seeing and feeling the power of the greats.
"I happened to have the privilege of fighting Frazier and Ali, and a few others, but those two to me were the greatest.
"Joe took everything away I thought I had and made me realise I needed more. If I was going to succeed I needed a lot more.
"It hit me like a lightning bolt when I heard he died."
Former world champion
Chris Eubank added: "In boxing, you look for an intense rivalry with men who are of the highest calibre in their abilities to fight.
"Muhammad Ali could not have been the mammoth character, fighter and man he became without Joe Frazier. He just couldn't have.
"You need someone to bounce off. You need another great. The operative word is great and indeed he [Frazier] was."
WBC champion
Vitali Klitschko said: "He was a huge fighter, huge champion and a huge personality.
"I didn't have a chance to see his fights live because I was born in 1971. In the Soviet Union, professional boxing was forbidden but we studied about this fighter and after that we had a chance to see the fights. It was a great lesson for all new generations.
"I didn't have a chance to meet him personally, but I heard about him and that's why he is always in the memory of the next generation of great fighters.
"From me and my brother [fellow world champion] Wladimir, I want to say sorry that he has died. He was one of the great champions."
Eight-time world champion
Manny Pacquiao said: "Boxing lost a great champion and the sport lost a great ambassador."
And five-time divisional world champion
Floyd Mayweather added: "RIP Smokin Joe. My thoughts and prayers go out to the Frazier family. We lost an all-time great tonight."
Promoter
Frank Warren believes Frazier's fights with Ali and Foreman mean the American will be remembered as one of the sport's finest.
"He was part of that era when we had the best heavyweights there had ever been," said Warren.
"People talk about Mike Tyson at the age of 21 - Joe Frazier, when he was a young fella, was every bit [as good as], if not better than, Tyson."
Continue reading the main story
Truth is, however much Frazier might have protested, Muhammad Ali illuminated Frazier's own greatness while also managing to be the bane of his life
Read more of Ben Dirs' blog
WBC light-heavyweight champion
Bernard Hopkins, a fellow Philadelphia fighter, said Frazier was an icon in the city and that he should have his own statue.
"There's no way in the world you should come to Philadelphia and not recognise who Joe Frazier is," he commented.
"It's the perfect time to build the biggest statue in appreciation for all the heart and love he gave to Philadelphia. We didn't realise we had a super-special person among us that we all, in a way, took for granted. I said this when he was living, I say this now."
Former welterweight and light-welterweight world champion
Ricky Hatton said that it is a very sad day for the world of boxing.
"The word 'legend' is sometimes passed around too easily in sport nowadays but the word 'legend' really does sum Joe Frazier up," Hatton told BBC Sport.
"He was a real throwback - fought the best, took on all-comers and was as brave as they come. They don't make heavyweights like Joe Frazier any more.
He would always come forward, everything was always a hook, hugely exciting and the era he boxed in was probably the most dangerous competitive era in heavyweight history."
Following the death of Joe Frazier, Mike Costello will take a journey back to the 1970s, when heavyweight boxing ruled the sporting planet, for a boxing special on BBC Radio 5 live Sport on Wednesday. You can listen to 'When They Were Kings' from 2130 GMT.
