Devils president and general manager Lou Lamoriello announced the signing on Tuesday without disclosing details.
Matteau, the son of former Rangers forward Stephane Matteau, was the 29th overall pick in June. Stephane scored two double-overtime goals in the 1994 conference finals as New York eliminated New Jersey en route to the Stanley Cup.
"Stefan Matteau is a size-and-strength power forward," Lamoriello said, "who we consider to be one of our top prospects."
The 18-year-old Matteau spent the past two seasons with the United States Development Program. The 6-foot-2, 215-pound forward skated in 46 games for the Under-18 squad in 2011-12, recording 15 goals and 32 points. He played for Team USA's Under-17 team in 2010-11, posting seven goals and 11 assists.
Matteau will play in the Quebec Major Junior Hockey League this season for the Blainville-Boisbriand Armada. His father is an assistant coach with that team.