A Fifa report seen by the Press Association says there is "overwhelming evidence" that Mohamed bin Hammam used bribery in his presidential campaign.
The ethics committee also stated that former Fifa vice-president Jack Warner was "an accessory to corruption".
Warner resigned from his role on Monday and quit all football activities.
As a result, football's governing body dropped all investigations into Warner, adding that "the presumption of innocence is maintained".
However, the full report of the ethics committee headed by Namibian judge Petrus Damaseb said there was "comprehensive, convincing and overwhelming" proof that bribes had been paid to officials to support Bin Hammam's campaign for the Fifa presidency, and that Warner had facilitated this.
Tory MP Damian Collins
“I believe Jack Warner should be made to answer these charges - it's not enough just for him to resign”
Both 68-year-old Warner, from Trinidad and Tobago, and Qatar's Bin Hammam, 62, were provisionally suspended on 29 May.
Bin Hammam withdrew as a candidate in the Fifa presidential race against Sepp Blatter on the morning of his ethics committee hearing on 29 May. Both Bin Hammam and Warner deny the allegations.
The 17-page Fifa report was faxed to Warner on 14 June. Three days later, he informed Fifa he was quitting.
The report obtained by the Press Association concludes that there was "compelling" evidence that Bin Hammam and Warner arranged a special meeting of the 25 members of the Caribbean Football Union [CFU] on 10 and 11 May in Trinidad and that, with their knowledge, cash gifts were handed over.
Statements from witnesses, contained in the report, said they were handed brown envelopes each containing 40,000 US dollars. One of the witnesses, Fred Lunn from the Bahamas, photographed the cash before returning it.
The document also stated that four witnesses claimed that Warner told the CFU delegates on 11 May that the "money for the 'gifts' allegedly distributed the day before had been apparently provided by Mr Bin Hammam".
Warner's evidence to the 29 May hearing is described as "mere self-serving declarations" and that he "failed to provide the Fifa ethics committee with a plausible explanation".
Bin Hammam said in a statement: "There is nothing I can say more than I deny the allegations and insist that I have not done anything wrong during the special Congress at Trinidad."
Damian Collins, the Tory MP who is campaigning for a reform of Fifa, believes the case against Warner should be re-opened.
"This makes Fifa's claim that Warner can be presumed innocent absolutely incredible," he said. "I believe Jack Warner should be made to answer these charges - it's not enough just for him to resign.
"This shows it was a big error of judgement by Sepp Blatter to call off the inquiry and cover this up.
"Fifa should also confirm Mohamed Bin Hammam should not similarly be allowed to resign in return for having the investigation dropped."