He added: "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."
The mixture of relief, even jubilation, at Blatter's resignation and caution for what comes next was echoed by many involved in the game, particularly in Europe and the Americas, home to some of Blatter's most vocal critics.
Romario, the Brazilian soccer legend turned senator, wrote on Facebook that Blatter's resignation was the "best news in ages" and that it "begins a new era for world football".
Arne Friedrich, a former player in Germany's national team, tweeted: "At least one good news around the #Fifa scandals. Will be exciting what else is going to come up shortly."
Among the most immediate issues facing the soccer body is who will replace Blatter, 79, who has run Fifa for 17 years.
Two obvious candidates come to mind: Jordan's Prince Ali bin al-Hussein, a Fifa vice-president whose challenge to Blatter fell well short of victory; and France's Michel Platini, who oversees the powerful European governing body, Uefa. Within an hour of Blatter's announcement, al-Hussein said he planned to run again.
Most European countries backed al-Hussein in the election, but if Platini were to enter the race, the Jordanian would have trouble mustering that key support.
A superstar on the field and polished character off it, Platini cuts a fine figure for the sport. He introduced financial reform to club soccer and expansion of the European Championship, the sport's second most popular competition. He presided over the 1998 World Cup organising committee in his homeland and served on Fifa's executive committee.
Platini, however, would face resistance from African and Asian factions, who are suspicious of European power. Overwhelmingly, they supported Blatter, in part because, under Blatter's rule, the World Cup was played on their continents for the first time - South Korea/Japan in 2002 and South Africa eight years later.
Others mentioned include three former candidates: Portugal's Luis Figo, a famous former player; Dutchman Michael van Praag, who, like Figo, withdrew from the race to consolidate opposition with al-Hussein; and France's Jerome Champagne, a former Fifa deputy-general.
The wild card is Kuwait's Sheikh Ahmad al-Fahad al-Sabah, a Blatter ally who criticised the raid by police on the Fifa hotel and questioned the US Government's motives.
As it stands, many countries will be reluctant to change a system in which Fifa spreads the wealth accumulated by World Cup profits. Under Blatter, the lack of oversight led to misappropriation of funds within individual federations, enriching executives at the expense of infrastructure and youth projects. Unless the culture changes, the new boss may end up the same as the old boss.
Whoever is elected will have to confront not only an organisation in transition but one that might have to decide whether to order a fresh vote for hosting rights to the 2018 and 2022 World Cups. In all likelihood, Russia will retain the next tournament - even if improprieties are discovered, switching the venue on relatively short notice is unrealistic. Qatar in seven years is another matter.
The ongoing investigations and the next election will set the course for not only future World Cups, but the future of Fifa's tattered authority.
The contenders
• Michel Platini (France)
The Uefa president had been widely tipped to take over as the new Fifa president, having fallen out with Sepp Blatter towards the end of his reign. Platini led the anti-Blatter vote at the recent election and is the favourite to replace him.
• Luis Figo (Portugal)
Put himself forward as a contender to take over from Blatter in the recent election but did not make it to the election after failing to secure the necessary support. Would be a high-profile candidate who could secure popular support, but not experienced in Fifa politics.
• David Gill (England)
The former Manchester United chief executive has no real experience of Fifa's internal politics but earned admiration for his determination to take a stance against Blatter last week, when he refused to take up his position on Fifa's Exco.
• Sheikh Salman bin Ebrahim Al Khalifa (Bahrain)
The president of the Asian Football Confederation is a powerful figure in world football who played a key role in helping Blatter win his election last week. Might struggle to gain support in Europe - but then again, he might not need it.
• Prince Ali bin al-Hussein (Jordan)
The man beaten by Blatter in last week's presidential election is joint-favourite to take over from the Swiss. Won 73 votes in the election - enough to force a second round of voting, although he stood down before that happened.
• Michael van Praag (Holland)
The former Ajax chairman announced his intention to stand against Blatter in January but fell short of mustering enough backers. Might be tempted to try again, although he is already 67 years old and may not be the "new face" football demands.
• Alfredo Hawit (Honduras)
Hawit was made president of Concacaf after the arrest and suspension from Fifa of Jeffrey Webb last week. Will be high-profile in the coming weeks as his confederation hosts the Women's World Cup and Copa America, which could give him a platform to stake his claim.
• Sheikh Ahmad al Fahad al Sabah (Kuwait)
The Kuwaiti joined Fifa's all-powerful executive committee last week - he will stay there for at least two years - and is a hugely influential figure, who could draw support from around the world. A strong early contender.
• Jerome Champagne (France)
Another candidate who initially put himself forward to challenge Blatter this year and who failed to gain the necessary backing. A former French diplomat, Champagne served as an executive at Fifa from 1999 to 2010 - which might make him the kind of "inside" candidate who would know how to work the Fifa machine.
• David Ginola (France)
The former Tottenham player was an unlikely candidate in the first place - his bid was sponsored by a bookmaker - but he is undeterred, despite failing to make the main election. He has announced he is standing again to replace Blatter.
- Bloomberg,Telegraph Group Ltd
