Spencer, 31, was the No. 26 pick in the 2007 draft by the Cowboys and played the first eight seasons of his career in Dallas. He had 22 tackles, one forced fumble and a half-sack in 13 games last season.
Spencer made the Pro Bowl in 2012 after setting a career high with 11.0 sacks, but was limited to just one game in 2013 because of a knee injury.
The Saints finished No. 28 in scoring defense and No. 31 in yards allowed last season.
New Orleans has had an eventful offseason on offense and defense. The Saints traded tight end Jimmy Graham to the Seahawks and also dealt wide receiver Kenny Stills to the Dolphins. They also signed cornerback Brandon Browner and running back C.J. Spiller.
- Paul Palladino