UEFA president Michel Platini was among those to praise Sepp Blatter's decision to resign as FIFA president on Tuesday.
Platini had personally asked his former mentor to resign last week in the wake of indictments against top FIFA officials on U.S. racketeering charges, but Blatter declined and went on to be re-elected to a fifth term as president on Friday.
But Platini was placated on Tuesday after Blatter revealed his decision to step down as soon as a successor can be found.
"It was a difficult decision, a brave decision, and the right decision," said Platini, who is the bookmakers' early favourite to replace Blatter in a special election.
Platini also got an early endorsement from the Russian Football Union's acting president Nikita Simonyan, who said he "suits the role of president of FIFA better than anyone else... [He is] a more prepared and experienced person.''
Jordan's Prince Ali Bin Al Hussein, who lost last week's election to Blatter, repeatedly declined to say if he'd run again but told CNN that the president's resignation was "the right move."
"I think we have to look to the future," said Ali. "I am at the disposal of all the national associations who want a change, including all of those who were afraid to make a change.''
Former Portugal star Luis Figo also ran against Blatter but withdrew before the election. Of all the candidates he spoke out most fiercely against Blatter and rejoiced in a statement following the resignation.
"A good day for FIFA and for football. Change is finally coming," he wrote on Facebook. "I said on Friday that the day would come sooner or later. Here it is!
"Now we should, responsibly and calmly, find a consensual solution worldwide in order to start new era of dynamism, transparency and democracy in FIFA."
Netherlands FA chief Michael van Praag, the other serious candidate leading up to the election, said the resignation is a good start.
"I wanted change for the FIFA and this may be a very big step in the right direction," he said.
U.S. Soccer president Sunil Gulati was a staunch supporter of Prince Ali's bid to unseat Blatter. He called the resignation "an exceptional and immediate opportunity for positive change within FIFA."
"I commend him for making a decision that puts FIFA and the sport we love above all other interests," Gulati said. "This is the first of many steps towards real and meaningful reform within FIFA. Today is an occasion for optimism and belief for everyone who shares a passion for our game."
England's Football Association chairman Greg Dyke had floated the idea of a boycott of the 2018 and 2022 World Cups if FIFA continued under the structure that led to the indictments.
Speaking on BBC Radio Five Live, Dyke said: "It is a good afternoon! I think it's brilliant for world football. This is the start of something new."
The president of the Qatar FA slammed Dyke's efforts in a statement -- along with a swipe at England's national team.
"Mr Dyke's instinct to immediately focus on stripping Qatar of the World Cup speaks volumes on his views concerning what will be the first FIFA World Cup to take place in the Middle East," said Sheikh Hamad Bin Khalifa Bin Ahmed Al Thani.
"Having already co-operated fully with [Michael] Garcia's investigation -- and been subsequently cleared of any wrong-doing -- we welcome the office of the Swiss attorney general conducting its own work into the bidding process for the 2018 and 2022 World Cups.
"We would urge Mr Dyke to let the legal process take its course and concentrate on delivering his promise to build an England team capable of winning the 2022 FIFA World Cup in Qatar."
Former Manchester United chief executive David Gill, who said last week he intended to resign from the FIFA executive committee if Blatter remained, has indicated he will now reconsider after Blatter's departure.
"Naturally, I fully welcome today's news as a major step forward for FIFA on the road to proper reform," he said in a statement released by the FA. "As I announced following the election at FIFA congress, I simply could not countenance serving on the FIFA executive committee alongside Mr Blatter. I respect his decision but am pleased he is standing aside and by the clear determination for real change within FIFA. This in turn allows me to reconsider my position.
"Having yet to confirm formally my resignation, I am more than willing to play my part in helping to bring about a positive future for FIFA and to work with the many people within the organisation who are only committed to developing and promoting the game around the world."
In Parliament, culture secretary John Whittingdale had also called for Blatter to step down. He said FIFA now had to implement its promised major reforms.
"Governments, national associations and international confederations, along with players and fans have all called for Sepp Blatter to resign in recent days," Whittingdale said. "We welcome his belated announcement today but this is only the beginning of the process of change we need to see from FIFA. I sincerely hope this is the first step to a new FIFA that can command the confidence and respect of the football world once again."
Much of the U.S. investigation focuses on bribes connected to tournaments in North and South America, and the presidents of both North America's CONCACAF and South America's CONMEBOL were among those arrested last week.
CONMEBOL vice president Wilmar Valdez of Uruguay called the resignation "a shock for the football world."
"What we were convinced of is that either on the long or short term, Blatter's presidency was not going to hold," he told TyC Sports in Buenos Aires. "FIFA needed changes and now we will have to see how the pieces fall together."
Chile football federation president Harold Mayne Nicholls said Blatter's resignation "took some time but the gesture was worth it."
"This is what the football world is asking for," he added. "More transparency is needed, more democracy in decision-making. They are very important points, that the re-election has dates, for example."
Former Brazil forward Romario also saluted Blatter's exit, writing on his Facebook page: "It is the best news of all time. Joseph Blatter's resignation as FIFA president is the beginning of a new era for world football."
FIFPro, the world players' union, called for professional footballers to have a significant say in the future of FIFA and the sport as a whole, calling for "flawless governance."
It said in a statement: "The world's professional footballers, through FIFPro, have a pivotal role to play in the structural overhaul of football. We are deeply committed to achieving this critical outcome in conjunction with all of the game's key stakeholders."