Williams, 17, was provisionally named in the Jamaica team for the 100 metres and 4x100 metres relay at the World Championships in Doha which start on Friday.
The IADP ruled that she will be "reprimanded with no period of ineligibility". Williams returned the positive test at the Jamaican trials in June and had faced the possibility of a four-year ban.
“The IADP finds that the athlete has established no significant fault or negligence as she was given tablets by her guardian and had no intention to cheat in her In-Competition sprint event on June 21, 2019," the IADP said in a statement.
I am a clean athlete, says Hassan
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“The IADP recommends that the athlete undergoes another education programme on Anti-Doping In Sports Rules.”
Williams's coach Ato Boldon said he was relieved that she had been exonerated and confirmed that she was due to fly in to Doha.
"I’m satisfied that the panel came to the right decision based on the evidence and based on what the IAAF rules and the WADA code is," Boldon told Reuters.
"I wouldn’t want what Briana has endured at her age to happen to my worst enemy," the former Olympic and World Championship medallist added.