The Falcons signed Davis in 2012 as an undrafted free agent out of East Carolina. He started his college career at Boston College, redshirting when Ryan was a senior for the Eagles.
Davis made his NFL debut last year in a blowout loss to the Tampa Bay Buccaneers. He suffered a knee injury in the same game.
Davis' fate seemed sealed as he exited the field following Thursday's final minicamp practice. He was reminded that the NFL was a business as he walked to the locker room wearing a scowl.
"I understand the nature of this league and this business,'' Ryan said before Davis was officially waived. "It's one of those things that there's always going to be people coming through the doors.''
Falcons coach Mike Smith made clear this week that the backup spot behind Ryan was wide open. With Davis waived, the Falcons now have Sean Renfree, rookie Jeff Mathews and Yates behind Ryan.
"We played against him a couple of years ago [and] he got the better of us when we were down there in Houston,'' Ryan said, referring to Yates. "I've met him a couple of times. Really nice guy. Looking forward to working with him and what he can bring to our group.''
"We're always trying to put the most competitive roster in place and give ourselves the best opportunity to win,'' Smith said of the trade. "This was an opportunity that came up for us. We feel like it's going to create a very competitive atmosphere where we need to have some competition.''
Yates was not on the field for Thursday's practice.