Zajac scored 20 goals in 2008-09 and 25 the following year before slipping to 13 in 2010-11. The injury limited him to two in the regular season last year.
The signing of Zajac comes roughly six months after the Devils lost Parise, their captain and a 31-goal scorer last season, to Minnesota via free agency. While Parise loved his stay in New Jersey, the desire to play in his home state led him to leave.
Lamoriello said there was no greater urgency to re-sign Zajac after losing Parise.
"You don't replace a Zach Parise, I've said that," Lamoriello said. "I don't apologize for saying that. He was an exceptional player, but you move on. It's part of the game. He was a player we wanted here. We have a couple of other free agents we will be doing everything to get signed but it will be done quietly and won't interrupt the season."
Right wing David Clarkson and center Patrik Elias can become restricted free agents after the season.
"At this point right now, training camp is the most important thing," Lamoriello said. "Each player focusing on that and not worrying about (contracts) is the most important thing. They know what we think of them. If it's after the season, it's after the season."