On the team's Twitter site coach Bill Belichick called Wayne a "true professional." Belichick also said "our parting was mutual."
Wayne, a 14-year-veteran who played his entire career with Indianapolis, was signed in late-August. Wayne is seventh in NFL history with 1,070 receptions.
Brady will also be short a key receiver from last year's Super Bowl run when the team placed Brandon LaFell reserve-physically unable to perform list.
With the "Deflategate" saga behind him, Brady will take the field after the team unveils its championship banner. A federal judge overturned Brady's suspension Thursday backed by NFL Commissioner Roger Goodell, saying the league had legal missteps as it punished Brady for his role in using underinflated footballs during the AFC championship game last season.
Brady still hasn't addressed the media since the decision was reached, but posted a statement Friday night on Facebook in which he said he was "pleased to be eligible to play," but added that he was "sorry our league had to endure this."
Belichick was asked Saturday morning when Brady would speak and replied: "You'll have to talk to our PR department about that. I'm just the coach, just trying to coach the team."
Offensive lineman Sebastian Vollmer said the team won't see a difference with Brady's situation settled.
"Yeah, again, he was there for preseason, so nothing really changes for us," he said.
The club also cut running back Jonas Gray, who had 201 yards in a victory at Indianapolis last November.
One player that remembered the nervousness of "cut-down" day was defensive back Malcolm Butler, an undrafted free agent last season who made the game-winning interception in the final minute of the Super Bowl win over Seattle.
"What I was thinking about then is: 'I know I was going to make this roster,'" he said. "It made it seem like I wasn't going to make it, but I had a feeling that I was."
He later joked that he was glad his phone never rang last year when the cuts were finalized.
In addition, they released defensive back Daxton Swanson and three rookies: defensive back Justin Coleman, linebacker Xzavier Dickson and safety Brandon King.
AP NFL website: www.pro32.ap.org and www.twitter.com/AP_NFL
Copyright 2015 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.