Terms of the deal were not disclosed by the team, but media reports indicate it's for six years and $24 million.
Henrique, 23, scored 11 goals in 42 games last season.
"It was an exciting day," Henrique told The (Bergen) Record's Tom Gulitti. "My family and I are excited about it. It's something you've been working for for a long time. I'm extremely happy with what the deal is and how things are looking going forward."
A third-round pick (No. 82) in the 2008 NHL Draft, he was a Calder Trophy finalist in 2011-12 when he scored 16 goals and finished with 51 points in 74 games. Henrique then helped the Devils reach the 2012 Stanley Cup Final by scoring series-clinching overtime goals in the Eastern Conference Quarterfinals against the Florida Panthers and the Eastern Conference Final against the New York Rangers.
In 117 regular-season games, the 6-foot, 195-pound center has totaled 27 goals and 67 points. He has five goals and 13 points in 24 Stanley Cup Playoff games.