The pair were cleared because neither was advised on taking vitamin supplements which may have led to them testing positive for the banned steroid nandrolone, chairman Fakhruddin Ibrahim told reporters in Karachi.
Akhtar, 31, and Asif, 23, were banned for two years and one year respectively by an internal Pakistani tribunal in Nov 1. Both denied taking any illegal substances.
"This appeal committee... holds that Shoaib Akhtar and Mohammad Asif will not be deemed to have committed a doping offence," said Ibrahim, a retired judge.
"The ban and punishment imposed by the earlier tribunal is hereby set aside as being contrary to the provision of laws."
The three-member committee made its decision by a 2-1 majority, Ibrahim said. The other members are former Test cricketer Haseeb Ahsan and doping expert Dr. Danish Zaheer.
Mercurial Akhtar, nicknamed the Rawalpindi Express, would have been ruled out of cricket until the age of 33 by the ban, threatening an international career already blighted by injury and indiscipline.
"I missed playing cricket for my country and now I hope that I will resume my career. The whole team had supported me and I am thankful to my teammates and every cricket lover who prayed for me," Akhtar told AFP.
"I am breathing again, my life was jolted no-end by the ban. I can't describe the feeling," said Akhtar, who would also have been ruled out of cricket until the relatively advanced age of 33 by the ban.
Asif, an emerging star before the ban, said his whole family had been in turmoil since the dope test results were revealed in October, causing the pair to be sent home from the Champions League.
"I am delighted to hear that I will be playing again. These two months have been the worst of my life and only today I resumed training," said Asif, adding that he had lost six pounds through worrying.
"I hope the bad days are over now. I badly want to play and it was only through the support of my captain Inzamam-ul-Haq and coach Bob Woolmer that I kept myself going," said Asif.
Investigations into the positive tests centred on the vitamin and health substances that the injured pair had taken in recent months.
Ibrahim said the committee found it was "clearly, plainly evident that (neither) Shoaib Akhtar nor Mohammad Asif were ever warned or cautioned against taking supplements."
Asif was only told to discontinue taking the supplements when he himself told team physio Darryn Lifson about them in August 2006, he said.
Neither player was "even provided with any international or local publication warning them against the use supplements," the committee found.
It was the committee's "considered view that Shoaib Akhtar and Mohammad Asif have successfully established that they had an honest and reasonable belief that the supplements ingested by them did not contain any prohibited substances."
They were cleared under a law on exceptional circumstances in the Pakistan Cricket Board's laws.
At the time the bans were imposed the International Cricket Council had praised the Pakistan Cricket Board and the initial drugs tribunal for their handling of the case and for imposing the penalties.
The committee chairman said he was "fully satisfied" that the appeals process "met the demand of justice".
"We have reached a consensus and the only note of dissent from Dr. Zaheer was that he wanted re-tests on both the players," said Ibrahim.