The federation's appeals court decided Saturday to clear Starace entirely and reduce Bracciali's ban to one year.
Bracciali's fine was also reduced by half to 20,000 euros ($22,500).
An initial ruling by the federation in August was based on a probe by judicial authorities in Cremona, Italy, where the players still face likely charges of criminal association.
In 2007, Bracciali allegedly discussed fixing a match in Newport, Rhode Island, with an accountant who was later arrested.
In 2011, an owner of a betting parlor who was later arrested was allegedly heard saying Starace agreed to fix the result of a final in Casablanca, Morocco.
Starace's career-high ranking was 40th in 2012, while Bracciali reached 49th in 2006.