According to court documents, Dennis Hastert agreed to pay $3.5 million to a person he abused when the victim was aged 14 and Hastert was working as a teacher and wrestling coach.
Prosecutors allege he abused five boys.
Dennis Hastert, 74, has admitted lying and breaking financial laws.
The plea represents a dramatic fall for the former senior Republican politician, who has had his portrait removed from the House of Representatives in the US Congress.
The alleged abuse happened while Dennis Hastert was working in Yorkville, a suburb of Chicago, between 1965 and 1981. Three of the victims were wrestlers on a team he coached.
He cannot be charged with abuse as the statute of limitations has expired in the cases.
One of the victims – referred to in court documents as Individual A – said Dennis Hastert had stayed with him in a motel room on the way back from a trip to a wrestling camp and touched him inappropriately.
Two of the others, aged 14 and 17, said Dennis Hastert abused them in the locker room at the high school in Yorkville.
All the victims “struggled and are still struggling” with what Dennis Hastert did to them, prosecutors argue. He made them feel “alone, ashamed, guilty and devoid of dignity”, they say.
Dennis Hastert, who retired in 2007 after serving as House Speaker for eight years, will be sentenced later this month for concealing the large sums of money he paid to Individual A to buy his silence.
Between 2010 and 2012 Dennis Hastert withdrew $750,000 in lump sums of $50,000 before learning of rules requiring banks to report large transactions.
After that he withdrew a further $952,000 in lump sums of less than $10,000 between 2012 and 2014.
Dennis Hastert was able to pay Individual A $1.7 million in payments of $100,000 before being questioned by the FBI in 2014 about his withdrawals.
One of the reasons he gave for the large withdrawals was that he was being blackmailed by someone making a false claim of abuse.
He agreed to let investigators record phone conversations he had with Individual A, but prosecutors said the “tone and comments” of Individual A in the conversations were “inconsistent with someone committing extortion”.
In a deal with prosecutors, Dennis Hastert admitted the charge of “structuring and assisting in structuring currency transactions” by removing small sums of money to avoid the transactions being reported.
However, the charge of lying to FBI investigators is set to be dropped.
Defense lawyers want Dennis Hastert to be spared jail because they say he is suffering from ill health.
Dennis Hastert is due to be sentenced on April 27.
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