Lamoriello didn't specify the terms of the deal, but The (Newark, N.J.) Star-Ledger reported it is for eight years at $46 million.
The signing of Zajac -- who missed most of last season with an Achilles injury but hit his stride in the playoffs -- was a priority for the Devils after losing high-scoring Zach Parise to free agency.
The 27-year-old racked up seven goals and seven assists over 24 post-season contests during New Jersey's run to the 2012 Stanley Cup Finals.
"During his time in New Jersey, Travis Zajac has become a solid, all-situation player and one of the core leaders of our hockey club," Lamoriello said.
In his six seasons with the Devils, Zajac has compiled 91 goals and 164 assists over 423 regular-season games.