A source told ESPN's Adam Schefter that it's a seventh-round pick.
The trade came hours after the Eagles announced they intended to release Barbre.
The Broncos will not surrender the draft pick if Barbre fails to make the roster, a source told ESPN's Jeff Legwold. Barbre will compete for a spot as a guard in Denver, which could have as many as four new starters on the offensive line.
"I don't see why not. I have played in multiple systems," Barbre told Denver7. "I know what they are trying to do there. It's up to me to pick up the terminology quickly.
"But I am excited to get there. This is a great opportunity."
Barbre, 33, started 12 games last season for Philadelphia, playing left guard and some right tackle. He missed part of the spring with a calf injury. When available, he shared first-team reps at left guard with second-year player Isaac Seumalo.
Seumalo is going into training camp as the starter, offensive coordinator Frank Reich revealed earlier Wednesday.
"Isaac's the starter and then there's just competition from there. That's the great thing about training camp, the great thing about this business: It's just so stinking competitive," Reich said. "It's what the guys love about it. It's what we love about it. So, again, it'll play itself out."
The trade came on the day veterans reported to camp.
"Allen Barbre is a pro's pro," Eagles executive Howie Roseman said in a statement issued before the trade was announced. "Not only did he help the team with his solid play as a starter at left guard, but his ability to step up and play multiple positions helped us battle through some difficult situations."
Also on Wednesday, the Eagles waived defensive end Marcus Smith, their first-round selection (26th overall) in the 2014 draft. Smith was due a roster bonus of nearly $600,000 on the third day of training camp. Philadelphia avoided paying that and gets about $1.5 million in cap relief with the move.
In a corresponding move, the Eagles signed linebacker Steven Daniels to a three-year deal.
ESPN's Tim McManus contributed to this report.