The decision could allow the 26-year-old to be named as a late addition to the French squad for Euro 2016 after coach Didier Deschamps lost defender Jeremy Mathieu on Saturday because of a calf injury.
Sakho was provisionally banned for 30 days after failing an anti-doping test following Liverpool's Europa League tie against Manchester United on March 17.
L'Equipe said that Sakho's lawyers had argued that a fat-burning drug that the player had used was not on the list of banned substances, meaning that he was not guilty of doping.
If found guilty of a drugs violation, the player would have faced at least a six-month ban.
The newspaper said Sakho was now free to play and would be officially cleared of any wrongdoing in "the coming days".
Liverpool declined to comment on Saturday.
Sakho was omitted from the original France squad for the Euro finals on home territory but Deschamps has until Tuesday to register his 23-man squad with UEFA.
Although Sakho has not played since Liverpool's Europa Cup quarter-final against Dortmund on April 14, he has been training on his own twice a day and has said he would be ready to play for France if required.
Deschamps's defensive plans have also been hit by injury to Real Madrid centre back Raphael Varane and the coach has already called up one replacement in Samuel Umtiti of Olympique Lyonnais.
France start their campaign against Romania on June 10, before facing Albania and Switzerland in Group A.
(Reporting by Julien Pretot and Neil Robinson; Editing by Clare Fallon)
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