The NFL had banned Brady for allegedly colluding to deflate balls during a play-off game, but on Friday a US judge ruled it had "legal deficiencies".
"I don't think it has been good for our sport, to a large degree, we have all lost," said Brady, 38.
He can now play on 10 September against the Pittsburgh Steelers.
In a Facebook post, he added: "While I am pleased to be eligible to play, I am sorry our league had to endure this.
"I can't wait to fully commit my energy and emotion to focus on the challenges of the 2015 NFL season.
"I want to thank my family, my friends, all of the fans, past and current players and my team-mates for the support they have given me throughout this challenging experience."
He added he hoped "the attention of NFL fans can return to where it belongs - on the many great players and coaches who work so hard every week, and sacrifice so much, to make this game great".
Media playback is not supported on this device
The NFL had banned Brady after investigating claims the Patriots had deflated match balls to gain an advantage in January's 45-7 play-off victory over Indianapolis Colts, which sent them to the Super Bowl.
Deflated balls are considered easier to throw and catch.
Brady, considered one of the best quarterbacks ever and entering his 16th season, maintains neither he nor the club did anything wrong.
The league has already fined the Patriots a record $1m (£660,000) and stripped the team of two draft pick following its 243-page report into 'deflate-gate'.
The report found Brady was "generally aware" of the scheme.
NFL commissioner Roger Goodell has said that the league will appeal the judge's ruling.
New England Patriots quarterback Tom Brady says he is sorry the NFL "had to endure" the "deflate-gate" scandal, after his four-game ban was overturned.