The American said 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 Mr Blazer.
The US justice department alleges they accepted bribes and kickbacks estimated at more than $150m (£97m) over a 24-year period.
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