Davis spent the past two seasons with the Browns after serving as defensive coordinator for the Arizona Cardinals from 2009 to 2010 and the San Francisco 49ers from 2005 to 2006. Cleveland operated out of a 4-3 scheme under Dick Jauron last season, but Davis has experience in the 3-4 alignment the Eagles plan to run in 2013.
The hiring of Davis will fill the final vacancy on Kelly's coaching staff.
Rapoport reported earlier this week that Philadelphia tried to interview Todd Grantham at least twice over the past few weeks, but the Georgia defensive coordinator declined because of the time crunch with Wednesday being National Signing Day.
Davis comes to the Eagles highly recommended, according to Geoff Mosher of Comcast SportsNet Philadelphia. He likely was given a good word from Pat Shurmur, the Browns' former head coach who was hired by Kelly last month as offensive coordinator.
Follow Marc Sessler on Twitter @MarcSesslerNFL.