Blazer, the former CONCACAF general secretary and a FIFA executive committee member from 1996 to 2013, made his revelation little more than 24 hours after Sepp Blatter announced he would be standing down as FIFA president as the corruption crisis in world football deepened.
"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," Blazer said in his testimony.
Blazer said he also facilitated a bribe in the awarding of the 1998 World Cup, which was held in France.
It is not clear whether Morocco or France made the payment, although Morocco have been named in the indictment as being prepared to bribe for 2006.
Blazer said in his testimony: "I agreed with other persons in or around 1992 to facilitate the acceptance of a bribe in conjunction with the selection of the host nation for the 1998 World Cup."
"I and others agree that I or a co-conspirator would commit at least two acts of racketeering activity.
"Beginning in, or around, 2004 and continuing to 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.
"While acting in our official capacities we agreed to participate in a scheme to defraud FIFA and CONCACAF on the right to honest services by taking undisclosed bribes."
Blazer said bribes and kickbacks were also commonplace in the CONCACAF tournaments run in North and Central America and the Caribbean.
The 70-year-old, now said to be seriously ill, revealed that he had accepted payments for the CONCACAF affiliated Gold Cups - equivalent to the European Championship or the African Cup of Nations - for a decade.
He claimed: "In and around 1993 and continuing through the early 2000s 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."
Blazer agreed to co-operate with the US investigation which has engulfed FIFA in the past week and led to Blatter resigning on Tuesday after 17 years at the head of world football.
Last week 14 people were indicted on charges of 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 150million US dollars over a 24-year period.