Amendola’s deal is worth $31 million, including $10 million guaranteed.
Amendola’s agreement comes hours after Welker left the Patriots for a two-year deal with the Denver Broncos.
The 27-year-old Amendola finished last season with 63 receptions for 666 yards and three touchdowns in 11 games for the St. Louis Rams.
He missed virtually all of the 2011 season after dislocating his left elbow in the opener, and then injuring a triceps muscle after returning to practice.
Amendola has 196 receptions for 1,726 yards and seven touchdowns in 42 career games.