Zajac was signed to an eight-year, $46 million contract with the Devils on Wednesday, ending any chance that New Jersey would lose its No. 1 centre after this season.
Devils president and general manager Lou Lamoriello announced the deal shortly after Zajac scored a power-play goal off a great pass from Ilya Kovalchuk in a scrimmage against Albany of the AHL.
"I want to be here," Zajac said. "I believe in this organization. I think it is a first-class organization. It's the environment I want to surround myself on and off the ice, and my family loves New Jersey. We like the people here. We like living here. With all that and the players and coaching staff, I think we have a great chance here to always be successful."
Zajac is going to have money, too. He will make $3.5 million this season, $5 million the next and $6.5 million in the four-year span from 2015-16 through 2018-19. His salary the final two seasons will be $5.75 million.
"He's developed himself into an all-situation, complete player," Lamoriello said. "He's one of our core leaders. He has been from day one. His play in the playoffs was certainly monumental for us. As far as him coming back it's quite evident what he means."
Lamoriello said the two sides had started to work on the new contract before the NHL lockout began in September. They finished it after the league and its players finalized a new 10-year collective bargaining agreement earlier this month.
"Now I can just focus on making sure I am at my best for the season and continue to improve," Zajac said after the scrimmage.
The 27-year-old Zajac is set to enter his seventh season with the Devils. An Achilles' injury limited him to 15 regular-season games last year, but the Winnipeg native stepped up in the playoffs and scored seven goals in helping New Jersey reach the Stanley Cup finals.
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 centre 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."