Bin Hammam life ban overturned by CAS
However, CAS said the decision did not amount to an "affirmative finding of innocence" for Bin Hammam, saying that FIFA's investigation had not been thorough enough, and that the case could be re-opened with new evidence.
FIFA said it noted the outcome "with concern" while Bin Hammam told the BBC World Service that he wanted to retire from football, saying he had seen "the ugly face" of the sport in the last year.
Qatari Bin Hammam remained suspended from the game after the Asian Football Confederation (AFC), which he previously headed, opened a disciplinary case against their former boss over alleged financial wrongdong earlier this week.
He was banned for 30 days, which was extended to a worldwide ban by FIFA on Wednesday.
"The CAS has upheld Bin Hammam's appeal, annulled the decision rendered by the FIFA Appeal Committee and lifted the life ban imposed on Mr Bin Hammam," the CAS statement read.
Bin Hammam, a former member of FIFA's executive committee, challenged Sepp Blatter for the presidency of football's world ruling body last year.
He withdrew his candidacy, and was then provisionally suspended, days before the June election over allegations that he had tried to buy the votes of Caribbean officials by handing them $40,000 each in brown envelopes at a meeting in Port of Spain.
Blatter was subsequently re-elected unopposed for a fourth term as FIFA president, while Bin Hammam was found guilty of breaking seven articles of FIFA's ethics code, including one on bribery.
He was banned for life and subsequently lost an appeal at FIFA. Proceedings against former CONCACAF president Jack Warner, also present at the meeting in Trinidad & Tobago, were dropped after he resigned his post.
CAS said the three-man panel voted 2-1 in Bin Hammam's favour but added that his behaviour was "not of the highest ethical standard."
"It is more likely than not that Mr. Bin Hammam was the source of the monies that were brought into Trinidad and Tobago and eventually distributed at the meeting by Mr Warner," said CAS.
"In this way, his conduct, in collaboration with and most likely induced by Mr Warner, may not have complied with the highest ethical standards that should govern the world of football and other sports," said CAS.
"This is all the more so at the elevated levels of football governance at which individuals such as Mr. Bin Hammam and Mr. Warner have operated in the past.
"The Panel therefore wishes to make clear that in applying the law, as it is required to do under the CAS Code, it is not making any sort of affirmative finding of innocence in relation to Mr Bin Hammam.
"It is a situation of 'case not proven', coupled with concern on the part of the Panel that the FIFA investigation was not complete or comprehensive enough to fill the gaps in the record."
CAS added: "In its conclusion, the Panel noted that FIFA was in the process of reforming its ethics committee and that, in the event new evidence relating to the present case was discovered, it would be possible to re-open the case, in order to complete the factual background and to establish if Mr Bin Hamman has committed any violation of the FIFA Code of Ethics."
"Frankly speaking, my wish is to quit," Bin Hammam told the World Football progamme on BBC World Service.
"I served football that long, more than 42 years, I have seen a very ugly face of the sport, envy, jealousy. I will not talk about the corruption.
"I have found myself in the last year. I have found Mohamed Bin Hammam, the man of the family, of his friends, of going back to my business. I have found peace in the last year, I wish I can continue like this."
"For me, peace and enjoyment is outside the football environment. I have one mission, one target is to clear my name, then I will say goodbye."
The decision is a further blow to FIFA, which is struggling to clean up its image after years of corruption allegations.
Last week, court documents were released which showed that former FIFA president Joao Havelange and former executive committee member Ricardo Teixeira took multi-million dollar bribes on World Cup deals in the 1990s.
Earlier this week, FIFA named two renowned crime-fighters from the United States and Germany to head the two divisions of its recently-reformed ethics committee.
FIFA said in its statement: "At FIFA level, all relevant files will now be handed over to the new FIFA Ethics Committee, which will start operating on July 25.
"The FIFA Ethics Committee will then decide based on the reports and evidence presented to it if any action is required to be taken against Mohamed Bin Hammam."