The Eagles sent offensive lineman Dennis Kelly to Tennessee to complete the deal.
Green-Beckham was the 40th pick out of Oklahoma in 2015. He never played for the Sooners, practicing for them but not suiting up in the year after he was dismissed from Missouri.
At 6-foot-5 and 230 pounds, Green-Beckham can be a difficult target to defend. He caught 32 passes for 549 yards as a rookie with four touchdowns. But in his second training camp this summer, he was maddeningly inconsistent with the Titans.
"Obviously he's made mistakes," Eagles general manager Howie Roseman said. "He's a kindhearted kid, and he has the right intentions. And that if you get a chance to really spend some time with him, you'll see that. He's not a locker-room cancer at all.
"He comes in with an opportunity. No promises have been made. We felt comfortable to bring him in here to compete. He's physically gifted. He's 6-5, he's 240, he runs a 4.4. He's got a rare skill set. Now, there's a reason that he's available at this time. He's got to get more consistent. But for us and where we are in development, we thought it was a risk worth taking."
Philly here I come! Much love to all my teammates, coaches and fans in Nashville. Thanks for everything. #BirdGang— Dorial Green-Beckham (@realdgb) August 16, 2016
The Eagles' best receiver, Jordan Matthews, is injured. They signed former Giants second-round pick Rueben Randle in the offseason to add depth and also have 2015 first-round pick Nelson Agholor and 2014 third-round pick Josh Huff.
In addition to signing Andre Johnson at the start of camp, the Titans added two receivers -- Miami free agent Rishard Matthews and fifth-round pick Tajae Sharpe -- under new general manager Jon Robinson.
They are precise route runners who rarely drop passes, a stark contrast to what they saw from Green-Beckham.
Green-Beckham is raw, but the Eagles clearly think he was worth the trade and will work to develop him in a way the Titans couldn't.
"They thought it was a good opportunity for [Green-Beckham], and we thought adding Dennis would be good for our football team," Robinson said. "We are moving on. I appreciate everything Dorial did when he was here. He bought in to what we were trying to do. But in the end we felt like this was the best decision for the team."
The Associated Press contributed to this report.