Former top Fifa official Chuck Blazer admitted that he and others on the executive committee had agreed to accept bribes in conjunction with the choice of South Africa as 2010 World Cup host.
The American says he also helped to arrange bribes over the 1998 event.
The admissions come in a newly released transcript from a 2013 US hearing in which he pleads guilty to 10 charges.
The US has launched a wide-ranging criminal case that engulfed Fifa and led President Sepp Blatter to resign.
The US prosecutors last week indicted 14 people on charges of bribery, racketeering and money laundering. Four others had already been charged, including 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.
The details of 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.
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.
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.
Blazer also says: "I and others agreed to accept bribes and kickbacks in conjunction with the broadcast and other rights to the 1996, 1998, 2000, 2002 and 2003 Gold Cups (the regional championship for national teams)."
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 seriously ill, 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.