With incentives, Robbins could make $12 million over three years, a source said.
The addition of Robbins at defensive tackle could make it easier for the Rams to be able to choose a quarterback such as Sam Bradford with the first pick of the draft instead of Ndamukong Suh or Gerald McCoy.
Former Giants defensive coordinator Steve Spagnuolo wanted the 32-year-old Robbins to help in the locker room and help anchor the defensive line.
Robbins, a former second-round pick of the Minnesota Vikings, came to the Giants in 2004 and stayed with them until last season.
Robbins, 6 feet 4 and 317 pounds, started 63 games during his six years with the Giants.
John Clayton is a senior NFL writer for ESPN.com.