General manager Ray Shero made the announcement Friday in completing John Hynes' staff.
The Devils hired Geoff Ward and Alain Nasreddine as assistant coaches earlier this week.
The 50-year-old Terreri has served as goaltending coach since 2009-10, after spending eight seasons in a similar role at the AHL level. He was a member of New Jersey's 1995 and 2000 Stanley Cup championship teams.
Hynes coached the Pittsburgh Penguins' AHL team at Wilkes-Barre/Scranton before he was hired earlier this month. Nasreddine will lead the Devils' defense, and Ward will handle the forwards and power play.
Adam Oates and Scott Stevens had served as co-coaches after Pete DeBoer was fired. Oates told the team that he would not be returning, while Stevens' future with the organization is uncertain.