Rafael Esquivel admitted receiving bribes in connection with the sale of marketing rights to tournaments.
He was among seven officials arrested at a luxury hotel in Switzerland last year.
More than 40 individuals and entities have been charged under the probe.
Fifa corruption crisis: Key questions answered
Who are the indicted Fifa officials?
Mr Esquivel - a former president of the Venezuelan Football Federation - was extradited to the US in March and had been due to stand trial with six other defendants next year.
He pleaded guilty at the federal court in Brooklyn to racketeering conspiracy, three counts of wire fraud conspiracy and three counts of money laundering conspiracy. He also agreed to hand over more than $16m (Â£13m).
The charges related to bribery schemes to market South American club tournament the Copa Libertadores as well as the Copa America, which features national teams.
Mr Esquivel faces a maximum sentence of 20 years in prison for each charge.
So far 19 people and two companies have pleaded guilty in connection with the US investigation.

Robert Thomson, 18, from Bellshill, was last seen on Friday 3 June and reported missing by his family two days later.
Police said the body found in woods near Kilbrennan Drive, Motherwell, had yet to be formally identified but was believed to be Mr Thomson.
A post-mortem examination will be held to establish the cause of death, which is not being treated as suspicious.

Khalil Dale, 60, was abducted in Quetta in January 2012 and was found dead on a roadside a few months later.
He had been beheaded. A note next to his body said he was killed because a ransom had not been paid.
Mr Dale was born in York but lived in Dumfries. He spent 30 years working in countries including Somalia, Afghanistan and Iraq.
An inquest into his death was held at Chesterfield Coroners Court because he is buried in Derbyshire.
The court heard that the Muslim convert, who was formerly known as Kenneth, worked as a humanitarian assistance relief worker.
Following his abduction, negotiations were undertaken by the International Committee of the Red Cross with the help of the UK government.
His body was found on 29 April 2012.
The inquest was told that he died as a result of decapitation.
Senior coroner Dr Robert Hunter concluded that Mr Dale was unlawfully killed while providing international humanitarian assistance.
A Venezuelan football official has pleaded guilty to corruption charges in the US as part of the investigation into the sport's world governing body Fifa.
[NEXT_CONCEPT]
A body found near Strathclyde Park in Motherwell is believed to be that of a missing teenager, police have said.
[NEXT_CONCEPT]
A Dumfries-based Red Cross worker who died in Pakistan was unlawfully killed, a coroner has ruled.