Galette reached terms with the team on Saturday. He had been set to become a restricted free-agent next week.
Galette was originally signed by New Orleans as an undrafted free-agent out of Stillman College in 2010.
In 2012, Galette appeared in 16 games with one start at left defensive end and finished with 22 tackles and a career-high five sacks.
After spending his first three seasons at defensive end, the Saints say Galette will move to linebacker in the new 3-4 alignment.
Copyright 2013 by The Associated Press