The Australian Sports Anti-Doping Authority (ASADA) said an extensive analysis of the evidence left no doubt about the negative finding.
"The evidence does not indicate the use of performance enhancing substances by Mr Thorpe," Richard Ings, the authority's chairman, told reporters.
"ASADA now considers the matter closed."
L'Equipe, the French sports newspaper, reported that Thorpe had returned abnormal levels of two banned substances from a urine sample he gave in May 2006.
Thorpe, who was so outraged at the allegations that he staged an impromptu press conference at the World Swimming Championships in Melbourne in April, welcomed ASADA's findings.
"My reputation as a fair competitor in swimming is the thing I value most," Thorpe said in a statement.
"I have always been, and remain, a strong supporter of anti-doping testing. I firmly believe drugs have no place in sport."
Former Australian swimmer Ian Thorpe
"I have always been, and remain, a strong supporter of anti-doping testing. I firmly believe drugs have no place in sport.
"I took my obligations to comply with the anti-doping codes very seriously and prided myself on this."
Thorpe, who is not currently in Australia, earlier this month presented ASADA with evidence and records to explain the elevated readings.
ASADA also took on-board expert advice from a number of organisations including the World Anti-Doping Agency (WADA) and accredited laboratories in Canada and Australia.
"Experts from these internationally respected organisations were unanimous in their opinion that the evidence available does not indicate the use of performance-enhancing substances by the athlete," ASADA said.
Thorpe dominated world swimming for eight years, winning a combined haul of five gold, three silver and one bronze medal at the 2000 Sydney and 2004 Athens Games, before he announced his surprise retirement on November 21, 2006.
The publication of the story in L'Equipe sparked an international hunt to find the source of the leak, which Thorpe's lawyer said damaged anti-doping efforts.
"While we stand by the testing process... Ian was denied his right to confidentiality due to an information leak, this breach of confidentiality jeopardises the integrity of the entire testing code."