Fifa president Sepp Blatter was aware senior officials were paid millions of pounds, according to a court investigation into bribery claims.
Former president Joao Havelange and executive committee member Ricardo Teixeira were named on Wednesday as having received huge sums by Fifa's former marketing partner ISL.
Neither were disciplined by Fifa.
Instead, Fifa paid £1.64m (2.5m Swiss francs) to a Swiss court on condition criminal proceedings were dropped.
On Fifa's website, Blatter says he knew about the payments but that they were legal at the time.
He said: "Back then, such payments could even be deducted from tax as a business expense. Today, that would be punishable under law.
"You can't judge the past on the basis of today's standards. Otherwise it would end up with moral justice. I can't have known about an offence that wasn't even one."
Switzerland's supreme court ordered the publication of the documents identifying which senior officials took millions of dollars in payments from ISL, which collapsed into bankruptcy in 2001.
The papers were released to five media organisations, including the BBC, and detail the compensation which closed the criminal probe in May 2010.
In November that year, the BBC's Panorama programme alleged that three senior Fifa officials, including Teixeira, took bribes from Swiss-based ISL in the 1990s, though commercial bribery was not a crime in Switzerland at the time.
The document states: "The finding that Fifa had knowledge of the bribery payments to persons within its organs is not questioned."
Havelange received at least £986,000 and executive committee member Ricardo Teixeira at least £8.4m.
The Swiss prosecutor's report, published by Fifa, reveals the pair may have received up to £14.4m.
They were the only two Fifa officials named in the report.
Havelange was Fifa president for 24 years before being succeeded by Sepp Blatter in 1998. The 96-year-old Brazilian, who remains Fifa's honorary president, has been treated extensively in a Rio de Janeiro hospital this year for septic arthritis.
He resigned his 48-year International Olympic Commitee membership, citing health reasons, in December - days before the Olympic body was due to sanction him following its own investigation into wrongdoing connected to ISL.
Teixeira, Havelange's former son-in-law, this year resigned as head of Brazil's football federation and the 2014 World Cup organising committee, and gave up his Fifa executive committee seat, citing unspecified health and personal reasons.