Braman became the second special-teams player that the Eagles signed Wednesday, joining Chris Maragos.
The 26-year-old Braman spent the last three seasons with the Houston Texans, recording 36 tackles.
"We are always looking for core special teams players and Bryan has made his mark in this league on those units," said Eagles general manager Howie Roseman.
"He was a Pro Bowl alternate two years ago. He's a big, physical player who plays with a tremendous amount of toughness."
During his career, Braman has also blocked two punts, both of which were returned for touchdowns, one by Braman himself.