Saints spokesman Greg Bensel says Strief, a restricted free agent this offseason, signed his tender offer from the club on Monday.
The Saints had offered Strief about $1.76 million.
Strief played in every game last season, starting twice at tackle during the regular season. He also subbed in routinely as a blocking tight end.
Strief, 26, was drafted out of Northwestern in the seventh round in 2006. He has played in 57 regular-season games, starting five. He also has appeared in all five of the Saints' playoff games since he joined the club.