Jack was banned by Swimming Australia for four years after testing positive for the muscle growth agent ligandrol in an out-of-competition test in June 2019.
She claimed it entered her system by contamination and has fought to clear her name.
Lausanne-based CAS, sport's highest court, concluded that "on the balance of probabilities" Jack "did not intentionally ingest ligandrol" and reduced her ban to two years dating from July 12, 2019.
That means that she could, in theory, compete in the postponed Tokyo Olympics that start on July 23, 2021. She would however be ineligible during the qualification process in the preceding months.