Morgan returns after a knee injury in training camp cost him all of last season.
Lorig joins New Orleans after spending his first four NFL seasons with Tampa Bay, where he also played tight end.
Financial terms have not been released for the deals, which were announced Tuesday.
Morgan began his career in New Orleans as an undrafted free agent in 2011 and made his regular season debut in 2012, when he caught 10 passes for 379 yards and three touchdowns.
Lorig has served as the lead blocker for a pair of 1,000-yard rushers. He also has 30 catches for 193 yards and a touchdown.
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