Former top Fifa official Chuck Blazer has admitted that he and others on the executive committee agreed to accept bribes in connection with the choice of South Africa as 2010 World Cup hosts.
The American said he also facilitated bribes over the 1998 event.
The admissions come in a newly released transcript from a 2013 US hearing in which he pleaded guilty to 10 charges.
The US has launched a wide-ranging criminal case that has engulfed Fifa and led president Sepp Blatter to resign.
Last week US prosecutors indicted 14 people on charges of bribery, racketeering and money laundering. Four others had already been charged, including Mr Blazer.
The US justice department alleges they accepted bribes and kickbacks estimated at more than $150m (£97m) over a 24-year period.
Seven of the 14 were top Fifa officials who were arrested in Zurich, Switzerland, as they awaited the Fifa congress. Two were vice-presidents.
In another development, former Fifa Vice-President Jack Warner, who is among those charged, said on Wednesday he had documents linking Fifa officials to the 2010 election in Trinidad and Tobago.
"I will no longer keep secrets for them who actively seek to destroy the country," he said in a paid political broadcast on Wednesday evening.
Mr Warner, who denies charges against him, said he feared for his life, but would reveal everything he knows about the alleged corruption.
The details of Mr Blazer's guilty pleas came as prosecutors unsealed the transcript of the 2013 hearing in the Eastern New York District Court. The admissions are part of a sentencing deal with prosecutors.
Mr Blazer was the second highest official in Fifa's North and Central American and Caribbean region (Concacaf) from 1990 to 2011 and also served on Fifa's executive committee between 1997 and 2013.
In the transcript, prosecutors refer to Fifa "and its membership or constituent organisation" as a Rico enterprise - a Racketeering Influenced Corrupt Organisation.
Mr Blazer says: "Beginning in or around 2004 and continuing through 2011, I and others on the Fifa executive committee agreed to accept bribes in conjunction with the selection of South Africa as the host nation for the 2010 World Cup."
Earlier on Wednesday, South Africa denied paying a $10m bribe to secure the hosting of the 2010 event.
Mr Blazer said one of his co-conspirators received a bribe in Morocco for its bid to host the 1998 tournament, which was eventually awarded to France.
He and others also accepted bribes in connection with broadcast and other rights to the Concacaf Gold Cup tournament in 1996, 1998, 2000, 2002 and 2003, he added.
Other admissions among the 10 charges in the 40-page dossier include US tax evasion.
Federal agents investigating the tax evasion had detained Mr Blazer and he agreed to co-operate in the US investigations.
He is said to have agreed to record his colleagues using a microphone hidden in a keychain.
The 70-year-old is said to be suffering from colon cancer.
In addition to the US case, Swiss authorities have launched a criminal investigation into how the 2018 and 2022 World Cups were allocated.
Qatar has said there is no way it will be stripped of the right to host the 2022 World Cup despite the corruption probe.
Foreign minister Khaled al Attiyah dismissed what he called "a bashing campaign" as anti-Arab prejudice and said Qatar was confident it could prove there had been no wrongdoing in its selection.
Earlier on Wednesday, Mr Blatter was given a 10-minute standing ovation by some 400 staff as he returned to Fifa's Zurich headquarters a day after announcing he was to step down.
Reportedly close to tears, he urged his "fantastic team" to "stay strong".
He emphasised the reform work that Fifa now needed to undertake.
In his resignation speech on Tuesday, he said that although he was re-elected president by the congress last Friday it appeared the mandate he had been given did "not seem to be supported by everybody in the world of football".