The deal is worth $11 million, with $6.5 million in guaranteed money, a source said. The overall value could grow to $11.7 million depending on how he performs, the source said.
Weaver was a restricted free agent and would have been available for a second-round pick. He was the NFC's Pro Bowl fullback last season after signing a one-year, $1.7 million contract.
Weaver had a career-high 323 yards rushing, 140 yards receiving and four touchdowns in his first season with the Eagles. He spent his first four years with Seattle.
The Eagles released star running back Brian Westbrook last week, leaving Weaver as the lone veteran in the backfield.
John Clayton is a senior NFL writer for ESPN.com. Information from The Associated Press was included in this report.