The 28-year-old has spent his entire seven-year career in Carolina after being selected in the third round of the 2008 draft.
"Making this move was difficult because Charles has been a large part of what we have done since I came to Carolina four years ago," coach Ron Rivera said in a statement. "He has always tried to do everything we have asked of him and worked extremely hard. He is an outstanding young man and we wish him the very best."
The free safety started 72 games in his first five seasons. He missed most of the 2013 season with an Achilles injury and took a pay cut this offseason.
Godfrey started in the slot last week and struggled against the Green Bay Packers (Pro Football Focus graded him as a -5.5 in coverage).