ESPN reported Thursday that Davis, a native of Spartanburg, S.C., has reached agreement with the Carolina Panthers on a five-year contract worth $15.5 million.
The team has not confirmed the agreement.
Davis, 29, was released by the Washington Redskins last month for salary cap purposes, but his physical up-the-middle running style was not a fit in the wide-open offense of Coach Steve Spurrier.
Also, sources said Spurrier was uneasy about Davis because of his penchant for fumbling.
From 1999-2001, Davis averaged 326 carries for 1,385 yards and 11 touchdowns. He had just 820 yards on 207 carries last season under Spurrier, and he misses four games with knee and shoulder injuries.
The Panthers targeted Davis after releasing veteran back Lamar Smith last month. Smith rushed for 737 yards and seven touchdowns last season for Carolina, but was granted a leave of absence following his drunk driving arrest in November.
"We have evaluated Stephen Davis," said Carolina Panthers Head Coach John Fox after Davis' visit last week. "We think he has the potential to be an impact back. He's got great numbers over his career. I have faced him on more than one occasion when I was with the New York Giants. He's a big, strong, physical back, and he's someone that we would be interested in on the free agency market."
Davis, a 6-0, 230-pounder, is third on the Redskins' all-time rushing list with 5,790 yards and 45 touchdowns. He was a fourth-round pick in 1996, and enjoyed his best season with the Redskins in '99, rushing for 1,405 yards and touchdowns.
He is the only running back in franchise history to rush for at least 1,000 yards in three consecutives seasons.