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.
Galette has appeared in 32 games with two starts for the Saints.
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