Johnson, whose knee injury shelved him for New Orleans' previous game at Carolina, played in seven games this season with one start.
The Saints needed Johnson to play a regular role while fellow fullback Erik Lorig, who is now healthy, worked his way back from a preseason ankle injury.
Johnson carried eight times for 22 yards and caught two passes, including a 13-yard touchdown reception.
Becton is a second-year pro out of Virginia Tech who played in one game last season with San Diego.
Becton's signing comes after right tackle Zach Strief played through a back injury at Carolina.
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