The ruling by CAS will cause huge embarrassment to FIFA, whose ethics committee imposed the lifetime ban one year ago.
The 63-year-old Qatari has been not proven innocent by CAS but the appeal has been upheld on the grounds of insufficient evidence.
FIFA can bring fresh proceedings against Bin Hammam if the revamped ethics committee has any new evidence.
Bin Hammam was found guilty by FIFA's ethics committee last year of paying bribes to Caribbean Football Union officials at a meeting in Trinidad last year while campaigning against Blatter for the FIFA presidency.
Jack Warner, who quit as FIFA vice-president after the scandal broke, told officials gifts of 40,000 US dollars each and totalling around 1million US dollars had come from Bin Hammam.
The CAS panel made its decision by a 2:1 majority and said in its ruling: "The CAS panel has not been presented with any direct evidence to link Mr Bin Hammam with the money's physical presence in Trinidad and Tobago, its transfer in a suitcase or otherwise to Mr Warner, and its subsequent offer to the CFU members for the purpose of inducing them to vote for Mr Bin Hammam."
The CAS panel added that "it is more likely than not that Mr Bin Hammam was the source of the monies" and that "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".
CAS stressed it was not finding Bin Hammam innocent but that the case was "not proven".
"The panel is doing no more than concluding that the evidence is insufficient in that it does not permit the majority of the panel to reach the standard of comfortable satisfaction in relation to the matters on which the appellant was charged," the ruling states.
Bin Hammam had been president of the Asian Football Confederation and he was provisionally suspended by that governing body earlier this week.
That followed an audit by Pricewaterhouse Coopers that centred on contract negotiations and payments to and from AFC bank accounts during Bin Hammam's presidency.
He was alleged to have breached a number of AFC regulations including relating to gifts and bribery. Sources close to Bin Hammam say the allegations are further attempts to tarnish his name.
Bin Hammam always claimed the FIFA action against him was retribution for having challenged Blatter for the presidency.
He had been a growing force in international football and displayed his power by being influential in Qatar's runaway victory in the contest to host the 2022 World Cup.
Some observers had believed he was on course to defeat Blatter until, less than a month before the election, he was accused of paying around 1million US dollars to officials from 25 Caribbean nations.
Witnesses testified that after being addressed by Bin Hammam at a specially-arranged meeting in Trinidad, officials were invited to pick up cash gifts of 40,000 US dollars per association contained in brown envelopes.
FIFA expressed concern over the CAS decision and revealed that the 30-day temporary suspension of Bin Hammam by the AFC had been extended worldwide by FIFA's disciplinary committee.
A statement said: "FIFA has noted with concern the decision announced by the Court of Arbitration for Sport (CAS) in the Mohamed Bin Hammam case."
The statement noted that the CAS verdict said Bin Hammam "is more likely than not.... the source of the monies", and that FIFA's reformed ethics committee could re-open the case if new evidence was presented.
The statement added: "Moreover, FIFA has taken note of the decision by the AFC earlier this week to open a disciplinary case against Mohamed Bin Hammam and to provisionally suspend him from taking part in any football activity for another matter.
"The chairman of the FIFA disciplinary committee extended this provisional suspension to worldwide level. Therefore, Mohamed Bin Hammam remains suspended until the current case has been concluded.
"At FIFA level, all relevant files will now be handed over to the new FIFA ethics committee, which will start operating on 25 July 2012. 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."
Eugene Gulland, speaking on behalf of Bin Hammam's legal team at Covington & Burling LLP, said: "We are delighted with the decision issued by the Court of Arbitration, rejecting all of FIFA's unfounded allegations of wrongdoing against Mr Bin Hammam, allowing his appeal and quashing FIFA's unjust life ban.
"Throughout this lengthy process Mr Bin Hammam has maintained his innocence and remained confident that he would be vindicated once the case was brought before an independent, third party body.
Bin Hammam stated in an interview that he would quit football once he had cleared his name of all charges.
He told the BBC World Service's world football programme: "I promise you I will not quit until I clear my name.
"I have one aim, one mission, one target and that is to clear my name and then I say goodbye."
Bin Hammam said the experiences of the last year had made him fall out of love with football.
He added: "Frankly speaking what my wish is, is to quit. I have served football more than 42 years and the last year I have seen a very bad, very ugly face of the sport and of the football.
"The jealousy... I will not talk about corruption and other things everybody is talking about. My wish now is just to quit and retire.
"When I have been falsely suspended I have really found myself: Mohamed Bin Hammam the man, the family man, the man of his friends, going back to my business, I have found peace in the last year and I wish to continue like it.
"I am 100% innocent in my actions in all the campaign and that was very important for me."