Previous bid chief Lord Triesman resigned on Sunday after the Mail on Sunday published transcripts from a recorded conversation in which he made serious allegations against the Russian and Spanish football associations.
Triesman suggested that the Spanish federation was willing to support Russia's bid for the 2018 tournament in exchange for assistance in bribing referees at this year's World Cup in South Africa to Spain's advantage.
In his resignation statement he distanced his words from the FA's position and asserted that they amounted to no more than private speculation.
Geoff Thompson was already the British FIFA vice-president and has previously served as FA chairman - the other position vacated by Triesman.
The official FA statement was as follows:
"Following the unanimous approval of the Football Association Board, Geoff Thompson has tonight been confirmed as the new Chairman of England 2018.
"Thompson, who is a vice-president on both the FIFA and UEFA Executive Committees, is England's most senior international football administrator.
"He was part of the five person delegation which delivered England's Bid Book to FIFA president Sepp Blatter in Zurich on Friday and was chairman of the FA for nine years between 1999 and 2008.
"He will take up his new role with immediate effect."
FIFA have yet to comment on the incident, but Russian bid chief Aleksey Sorokin called on the world governing body to "take appropriate measures".
"It is a sign that we are going in the right direction, that the quality of our bid leaves no other alternative for our competitors but to bring up these absurd allegations," he told Sky Sports.Sebastian Coe, who led the bid team for the London 2012 Olympics and is on the board of the FA's 2018 bid, has already briefed FIFA general secretary Jerome Valcke on the situation and is due to speak to FIFA president Sepp Blatter.
He said Sunday's revelations need not derail the campaign to bring the World Cup to England.
"This has been a traumatic 48 hours but this does not become a bad bid overnight," Coe told the Press Association.
"Solid foundations are in place, we have the best venues, the most passionate fans, the best market for sponsors and an unparalleled ability to deliver this tournament in safe and secure surroundings.
"The only thing we don't have is the private views of the former chairman."
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