The 10-year veteran played the last three seasons with the Buffalo Bills, including 2014 under defensive coordinator Jim Schwartz, who currently has the same title with the Eagles.
Graham was a cornerback for a good portion of his career before switching to safety, where he started every game the past two seasons for former Bills coach Rex Ryan.
The Eagles listed the 32-year-old Graham as a safety in their release announcing the move.
Schwartz has talked a lot recently about the need for versatile players to combat, among other things, the "proliferation of the wide receiver tight end." Graham might be able to find a role as a hybrid safety/nickel in sub packages.
The Eagles' primary safety spots are spoken for with Malcolm Jenkins and Rodney McLeod. Cornerback is the more pressing need, as the position group that features Jalen Mills, Patrick Robinson, rookie Rasul Douglas and Ron Brooks is considered one of the shakiest in training camp.
"We're very interested in the cornerback competition," Schwartz said. "It's a daily thing for those guys. And we need not only playmakers, but we need consistency."
He has 603 tackles, 15 interceptions and 60 passes defensed in 10 NFL seasons. He was selected for his only Pro Bowl in 2011, while with the Bears.
ESPN's Mike Rodak contributed to this report.