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In charge of world football's governing body since 1998, Blatter, 79, said last year he was standing down amid a growing corruption crisis.
Five candidates want to replace him.
They are Sheikh Salman bin Ebrahim al-Khalifa, Gianni Infantino, Prince Ali bin al-Hussein, Tokyo Sexwale and Jerome Champagne.
The election process is expected to begin at 12:00 GMT, but several rounds of voting may be required before a winner is known.
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Each candidate has 15 minutes to address the congress before voting starts at approximately 12:00 GMT.
There are 209 Fifa nations but Kuwait and Indonesia are currently barred from taking part, so that makes 207 eligible voters.
To become president after the first round of voting, a candidate needs to secure two-thirds of the available votes. If no candidate achieves that mark, then a simple majority is required in the second round.
If there is still no winner, then a third round will take place, minus the candidate with the fewest votes in round two.
Fifa says a winner must be declared on Friday because an ice hockey rink is due to be installed at the Hallenstadion venue at midnight.
So determined is Fifa to get this election done that it has spent £500,000 converting its headquarters into a back-up venue.
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Given everything that has happened to Fifa, this is seen as a pivotal moment for an organisation which has been heavily criticised for its lack of transparency and for failing to clamp down on corruption within it.
A new leader, together with a raft of reform measures, is seen as a chance to start afresh.
Acting president Issa Hayatou said Friday can "signal a new dawn", adding: "This is our opportunity to show we are united in building a stronger Fifa."
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There have been widespread allegations of corruption, the arrest of leading officials, the banning of its president and the sight of big-name sponsors deserting the organisation.
Numerous Fifa officials have been indicted in the United States, while Swiss authorities are also investigating the organisation.
Blatter has also been banned from all football activity for six years after being found guilty of breaching Fifa's ethics rules over a $2m (£1.3m) "disloyal payment" to the head of European football's governing body Uefa, Michel Platini, who had been favourite to succeed the Swiss.
Former France captain Platini was also suspended. Both men deny any wrongdoing and are appealing to the Court of Arbitration for Sport.
Furthermore, Jerome Valcke, Fifa's secretary general and formerly Blatter's right-hand man, was banned for 12 years following allegations - which he denies - of misconduct while in office.
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Fifa's leader is the figurehead for world football, often seen in public alongside presidents, prime ministers and royalty.
There have been eight of them so far, presiding over the organisation's executive committee, which is where the real decision-making power lies.
Fifa organises World Cups and other international tournaments, distributes broadcasting rights and should both protect and develop the world's most popular sport.
The president also "legally represents" the organisation, "maintains relations between Fifa and the confederations, members, political bodies and international organisations", and "implements the decisions passed by the congress and the executive committee".
There are five candidates, from Africa, Europe and the Middle East:
Prince Ali bin al-Hussein
Jerome Champagne
Gianni Infantino
Sheikh Salman bin Ebrahim al-Khalifa
Tokyo Sexwale
Read more: the five candidates profiled
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Prince Ali: "I'm a candidate beholden to no one. I wouldn't apply political pressure or coercion. I'm the only candidate from a national association."
Infantino: "I'm not a politician, I'm football person and I'm a worker. If we stop doing politics and start doing football, the world will admire us."
Sheikh Salman: "My past and my track record speaks for itself. We want someone who is responsible and can deliver the promises he says."
Champagne: "I want a Fifa that serves football, that serves you. The Fifa I dream of is one which correct the inequalities."
Sexwale: "I'm here, despite any obstacle. My life experience as a fighter, someone who dies wearing his boots... I have come this far."
Prince Ali wants to quadruple the amount Fifa's member associations receive - believing it will increase their sustainability - but wants the money properly accounted for.
Infantino would expand the World Cup to 40 teams to ensure more smaller nations can participate. He also wants to hugely expand Fifa's development plan by investing £860m of its revenues and giving £3.6m to each member association.
Sheikh Salman's big idea is to split Fifa in two with a business side handling commercial issues and the football side organising World Cups and developing the game. He believes this would stop executives making self-interested decisions.
Champagne's most recent manifesto, Hope For Football, emphasised "rebalancing" the inequality in football and "reconciling" the game's "protagonists". He wants to modernise - by introducing technology to help referees, having women in key Fifa roles and run Fifa like a public sector organisation.
Sexwale has focused on his background in administration in the election run-up. His manifesto headline was the idea to put sponsors on national teams shirts to help raise money for the football associations.
Sheikh Salman is the front runner because he has the backing of his own Asian confederation, as well as Africa.
The continents do not vote as a block and the ballot is held in secret.
But such political backing from two of the biggest confederations should not be underestimated and may not be hard to deny.
Infantino, who is effectively in charge of European football following the suspension of Uefa president Platini.
The 45-year-old has, according to his camp, made gains in recent weeks and they believe he is the man to beat.
On Thursday, Infantino told BBC Sport he was expecting 105 out of 207 votes in the first round - the same as Salman predicts for himself.
Uefa's general secretary has strong support in Europe and South America, as well as significant backing in the potentially crucial Caribbean and his camp also thinks he will get half the votes in Africa.
If those predictions prove true, he will win.
Prince Ali lost out to Blatter in last year's election and looks like missing out again after failing to make gains after Platini was banned.
However, if he does drop out and asks his supporters to back a rival candidate he could still be an important influence in deciding the eventual winner.
As for Champagne and Sexwale, who is a former political prisoner on South Africa's Robben Island, they are the rank outsiders.
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The delegates are also being asked to agree to reforms designed to end the problems that have led to Fifa's crisis in recent months and restore the organisation's reputation.
Specifically, Fifa wants members to agree to term limits for top officials along with disclosure of their salaries.
Another proposal is to disband Fifa's executive committee and replace it with a 36-member Fifa council, which will include a minimum of six women.
Greg Dyke, who will cast a vote as chairman of the Football Association, says the reforms are "more important" than the new leader as it will provide an "opportunity for Fifa to start again".
BBC sports editor Dan Roan in Zurich:
"Few fans or players would recognise these individuals, let alone know about their policies or have trust in their leadership.
"The selection of Sepp Blatter's successor should be the moment the governing body finally consigns the tainted tenure of their former president to history, and symbolically moves on from the stranglehold he held over the organisation for so long.
"Except to many, it simply does not feel like that.
"All of the men running for president are members of the football establishment. Four of them have spoken to Blatter in the build up to the election, presumably to ask for advice. All are loathe to condemn the disgraced former president.
"The next 24 hours matters a great deal, and much is at stake. But do not assume that it represents the end of this great scandal, or the solution to FIFA's troubles. We should all know better by now."
Read Dan Roan's full blog here
Fifa will get a new president on Friday when 207 delegates from around the world gather in Zurich, Switzerland to vote for a successor to Sepp Blatter.