Jones, a nine-year veteran, is fifth all-time in gross (45.6 yards) and net (39 yards) punting averages. He played last season for the Houston Texans and was a two-time All-Pro pick for the St. Louis Rams (2008-09). He also has played for the Miami Dolphins and Seattle Seahawks.
Last season for the Texans he set franchise marks for gross (47.1) and net (40.5) punting averages. On Saturday, the Texans signed Shane Lechler to punt for them in 2013.
"Donnie Jones is a guy that we have admired over the last several years," Eagles general manager Howie Roseman said in a statement. "He has one of the strongest legs in the entire NFL and we're excited we had a chance to sign him. We watched a lot of tape on him and he's coming off a very good season with Houston. We feel he'll add a good element to our special teams units."
McBriar played in 13 games for the Eagles last season and averaged 46.5 yards per punt.
"Mat was nothing but a consummate professional for us in 2012. He battled back from a tough injury situation to punt very well last year. We just decided to go in a different direction with Donnie and we wish Mat and his family all the best as he continues his NFL career," Roseman said in the statement.