Braman, 26, has 36 special-teams tackles in 46 games.
A former undrafted free agent, Braman is a 6-foot-5, 241-pounder.
He's blocked two punts.
"You don't find many players of Bryan's size with the ability to run down the field and make plays on special teams," Eagles coach Chip Kelly said in a statement. "It's an area of the game that we always have our eye on and look to improve. With his size, we also like his potential as a guy who can compete for spot as an outside linebacker."
"We are always looking for core special teams players and Bryan has made his mark in this league on those units," Eagles general manager Howie Roseman said. "He was a Pro Bowl alternate two years ago. He's a big, physical player who plays with a tremendous amount of toughness."
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Aaron Wilson covers the Ravens for The Baltimore Sun