Sepp Blatter is to stand down as Fifa president amid reports he could face a corruption investigation by the FBI.
Officials in the US told the New York Times the 79-year-old is a focus of a probe by federal authorities, who the newspaper said were hoping to gain the co-operation of senior Fifa figures arrested last week.
Mr Blatter's resignation was welcomed by UK politicians, with Culture Secretary John Whittingdale calling it "belated" and "only the beginning of the process of change we need to see".
The departure of the head of world football's governing body came just days after being re-elected to the role - despite the indictment of current and former senior Fifa officials on suspicion of decades of bribe-taking.
At a hastily-arranged press conference Mr Blatter, who has held the role for 17 years, called an extraordinary congress "as soon as possible", saying "a new president will be elected to follow me".
The election is to take place between December and March and Mr Blatter will remain in position until then.
Uefa president Michel Platini, who led calls for Mr Blatter to resign last week, and Prince Ali Bin Al Hussein, who stood against the Swiss in last week's election, are among the names who have been tipped to run.
Other potential successors include former Newcastle and Tottenham winger David Ginola, who has said he intends to stand despite not winning a single nomination ahead of this year's race, and Sheikh Salman Bin Ebrahim Al Khalifa, the head of Asian football confederation.
Mr Blatter's announcement came after Fifa admitted it paid 10 million US dollars destined for the South Africa World Cup to an account controlled by disgraced former vice president Jack Warner. The payment followed a letter from the South African Football Association to Fifa secretary general Jerome Valcke.
Prime Minister David Cameron was among those who had publicly called for him to go amid widespread demands from critics for the controversial decisions to award World Cups to Russia and Qatar to be reopened.
Mr Whittingdale said: "Governments, national associations and international confederations, along with players and fans, have all called for Mr Blatter to resign in recent days.
"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."
Mr Whittingdale said last week that the Government and the Football Association (FA) have not ruled out any options in the battle to end the "culture of kickbacks and corruption that risk ruining international football for a generation".
Amid calls for a boycott of the World Cup, he assured MPs that the Government would do anything in its power to bring about change in world football's governing body.
Two FA directors have resigned Fifa posts and FA chairman Greg Dyke said the resignation was "great news for football".
"I think it is long overdue but it is good news for world football," he said.
"It now means that we can get someone in to run Fifa, we can get in there and find out where all the money has gone over all these years and sort it out for the future."
Shadow culture secretary Chris Bryant said the hugely-controversial decision to award the 2022 World Cup to Qatar should be reopened.
"This is great news for football. I'm glad Sepp Blatter has listened to the overwhelming calls and taken the inevitable decision to go," he said.
"His departure is necessary but not sufficient. Fifa needs complete reform, and to rerun the 2022 World Cup bid.
"The election of a new president needs to happen as soon as possible to give Fifa a chance to clean up its game and regain its reputation."