Thompson takes over as 2018 chair
Thompson, a vice-president on both the FIFA and UEFA executive committees, is an experienced international football administrator and was chairman of the FA from 1999 to 2008.
"Following the unanimous approval of the Football Association Board, Geoff Thompson has tonight been confirmed as the new Chairman of England 2018," a statement said.
He is already a key player in England's bid to host the World Cup for the first time since 1966 and was part of a five-man delegation that presented the bid book to FIFA headquarters in Zurich on Friday.
Triesman resigned as FA and 2018 bid chairman earlier on Sunday after a secretly recorded private conversation with a former colleague was published in the Mail on Sunday.
The 66-year-old was reported to have suggested that Spain and Russia, two rivals bidders for the 2018 World Cup, were involved in a conspiracy to bribe referees at next month's World Cup in South Africa.
London's Olympic organising committee (LOCOG) chairman Sebastian Coe may also play a more high-profile role in the 2018 bid.
"This has been a very unhappy episode," Coe, an avid Chelsea fan, was quoted by website Inside the Games on Sunday.
"But nothing changes. We have the best bid, the best fans, the best stadiums. The only thing that has changed is that we don't have the private views of the previous chairman."