The NFL banned Brady in May 2015 after he was deemed to have been aware that members of the Patriots' equipment staff had deflated footballs in his side's AFC Championship win over the Indianapolis Colts.
The Appeals court has sided with the league and has released a 33-page document explaining its decision.
One section reads: "We hold that the commissioner properly exercised his broad discretion under the collective bargaining agreement and that his procedural rulings were properly grounded in that agreement and did not deprive Brady of fundamental fairness. Accordingly, we reverse the judgement of the district court and remand with instructions to confirm the award."
Brady is expected to miss the Patriots' opening four games of the season against the Arizona Cardinals, Miami Dolphins, Houston Texans and the Buffalo Bills.