McBriar was a two-time Pro Bowl selection in eight seasons with the Cowboys.
Eagles' rookie Chas Henry averaged 42.9 yards per punt with a net of 36.9 in 2011.
Philadelphia must make a corresponding roster move by 4 p.m. ET.
McBriar, a native of Australia, has a career net average of 38.4 yards and led the league in punting in 2006 with a gross average of 47.9 yards and a 41.7-yard net.