The decision by the New England Patriots quarterback was confirmed Monday by the NFL Players Association, which is filing the appeal on his behalf. If the appeal is denied by the full panel, Brady could try to take his case to the U.S. Supreme Court.
In a statement, NFL Players Association Executive Director DeMaurice Smith said: "He was not afforded fundamental fairness and due process as guaranteed by the collective bargaining agreement and case law. We also know that the NFL propped up a now completely de-bunked 'independent' report with a made-up standard as the basis for his suspension."
The court ruled 2-1 on April 25 that Commissioner Roger Goodell was within his rights to suspend Brady for four games for his role in using improperly inflated footballs in the 2015 AFC championship game.
Brady has added lawyer Ted Olson to his legal team. Olson and union chief DeMaurice Smith appeared on ABC's "Good Morning America," saying they plan to ask for a new hearing before the entire 13-judge circuit.
At oral arguments in March, appeals judges seemed skeptical of arguments on Brady's behalf by the NFL Players Association.
Circuit Judge Denny Chin said evidence of ball tampering was "compelling, if not overwhelming" and there was evidence that Brady "knew about it, consented to it, encouraged it."
The league argued that it was fair for Goodell to severely penalize Brady after he concluded the prize quarterback tarnished the game by impeding the NFL's investigation by destroying a cellphone containing nearly 10,000 messages.
Judge Barrington D. Parker said the cellphone destruction raised the stakes "from air in a football to compromising the integrity of a proceeding that the commissioner had convened."
"So why couldn't the commissioner suspend Mr. Brady for that conduct alone?" he asked. Parker added: "With all due respect, Mr. Brady's explanation of that made no sense whatsoever."
Parker also was critical of the NFL at the arguments, saying Brady's lengthy suspension seemed at "first blush a draconian penalty."
Earlier this month, a group of Patriots fans unsuccessfully sued the NFL in an effort to recover the first-round draft pick taken from the team as punishment for the scandal.