A warrant was issued for the now 22-year-old in October last year after allegations were made in the wake of the Pan-Am Games tournament.
But a statement by the player's counsel on Tuesday said the charges had been dropped.
Brian Greenspan and Robin McKechney said an "unsupportable and irresponsible allegation" had been made which had "unfairly tarnished" the Brazilian.
The statement added: "The decision to withdraw the charge - on the basis that there was no reasonable prospect of conviction - reflects the thorough and professional examination of this matter by senior and experienced Crown prosecutors. The Crown's guidance had been sought - but clearly ignored - by the police prior to their October press conference.
"It is both regrettable and unacceptable that the police chose to disregard the balanced and fair-minded assessment made by the Crown, and to defiantly proceed to announce charges when the conclusion had been reached that the evidence could not justify a trial."
Piazon, who joined Chelsea from Sao Paulo in 2011, has scored two goals in eight appearances for Reading this season.
