The moves announced Wednesday came a day after Philadelphia added former Saints safety Malcolm Jenkins on the first day of NFL free agency.
Maragos and Braman bolster the special teams units for the defending NFC East champions.
Maragos began his career with San Francisco as an undrafted free agent in 2010 and spent the last three years in Seattle. He was a core player on special teams for the Super Bowl champion Seahawks last year.
Braman also was an undrafted free agent and played three seasons in Houston. He was a Pro Bowl alternate on special teams in 2012.