Weaver's deal was announced Friday, the first day of the NFL's free agency period. It reportedly is worth $11 million, including $6.5 million guaranteed.
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.