The Swiss official, who has ruled football's governing body for 17 years, said on Tuesday that he would remain in charge until a special congress can choose a new leader and vowed to pursue strong reforms in that time.
Blatter noted that he had just won re-election from Fifa members on Friday, but said: “I do not feel that I have a mandate from the entire world of football.”
Some of Blatter's opponents rejoiced at his announcement while commercial sponsors urged Fifa to clean up its act and regain public trust.
“Why didn't he step down last week? Clearly there's a smoking gun of some sort,” English Football Association chief Greg Dyke said.
“He's not been honourable in years. Now he's gone — let's celebrate.”
Uefa head Michel Platini, a former ally who last week told Blatter to his face that he should leave, said: “It was a difficult decision, a brave decision, and the right decision.”
Brazilian legend Pele called for “honest people” to clean up the game, while New Zealand Football made it clear that Blatter was not welcome at the Under-20 World Cup currently being held there.
“These allegations are hotting up, they're getting closer and closer to him,” NZF chief executive Andy Martin said.
The New York Times, which broke news of the corruption investigation, reported the 79-year-old was also the focus of an FBI probe, citing law enforcement officials and other sources.
ABC News also said Blatter was the subject of an investigation, which it said was part of the larger probe that led to the arrest of seven Fifa officials in a luxury Swiss hotel.
That unleashed a global storm which Blatter tried to weather by defiantly ploughing on when he secured a fifth term with backing from Asia and Africa.
But speaking impassively at Fifa headquarters in Zurich, Blatter said it was clear not everyone was on his side in the footballing fraternity including “the fans, the players, the clubs, the people who live, breathe and love football as much as we all do at Fifa”.
“I felt compelled to stand for re-election, as I believed that this was the best thing for the organization,” Blatter told a news conference.
“That election is over but Fifa's challenges are not. Fifa needs a profound overhaul,” he said, vowing “far-reaching, fundamental reforms” in his remaining time in office.
A special congress to choose Blatter's replacement cannot be held until between December 2015 and March 2016, according to Domenico Scala, chairman of Fifa's independent audit and compliance committee.
The seven people detained last Wednesday are among 14 football officials and sports marketing executives accused by US prosecutors of complicity in giving or receiving more than $150 million in bribes.
The dawn arrests, and a police raid on FIFA headquarters, were accompanied by the launch of a Swiss investigation into the awarding of the 2018 and 2022 World Cup tournaments to Russia and Qatar.
The US probe is also looking at a $10 million payment made by Fifa to South Africa, host of the 2010 tournament, which was reportedly approved by Blatter's top lieutenant.
Jordanian royal tipped
Blatter has repeatedly pleaded his innocence and that of Fifa.
Qatar has also strongly denied any wrongdoing in its bid for 2022 but one senior Qatari official, a Fifa vice president, was banned for life amid accusations that he gave bribes.
“If I was in Qatar I wouldn't be very confident,” said Dyke, who was involved in England's unsuccessful bid to stage the 2018 edition.
Acting Concacaf president Alfredo Hawit — who last week replaced former chief Jeffrey Webb, one of those charged in the United States and arrested in Switzerland — said his organization was ready to help rebuild Fifa.
That was echoed by the AFC in Asia, whose members comprise the third-biggest voting bloc for the Fifa leadership, behind Africa and Europe.
Jordan's Prince Ali bin al Hussein, who challenged Blatter in last Friday's vote, signalled that he would run again.
“If somebody's going to beat Prince Ali then they're going to have to be very good,” said New Zealand's Martin.
Other potential replacements mooted include Platini and Portuguese football great Luis Figo.
Among key sponsors, Coca-Cola called the move “a positive step for the good of sport, football and its fans”.
South Korean auto group Hyundai-Kia urged Fifa now to create “a governance structure that ensures the highest ethical standards for the sport”.
Credit card giant Visa, which had warned it might withdraw its sponsorship, said Blatter's resignation was “a significant first step” but added: “More work lies ahead.”