Elias' agent, Allan Walsh, announced the terms of the deal on Twitter.
Elias has spent his entire 15-year career with the Devils. He leads the franchise with 375 goals, 555 assists and 930 points in 1,090 career games. Elias holds career franchise playoff records with 45 goals, 80 assists and 125 points.
He has led the Devils in points in eight seasons, including this past year when he finished with 36 points (14 goals, 22 assists) in 48 games.
Selected by New Jersey in the second round of the 1994 draft, the Czech-born player has topped 70 points in a season five times. That included 2011-12, when Elias had 78 points (26 goals, 52 assists) in 81 games.
New Jersey also re-signed veteran forward Dainius Zubrus to what is reportedly a three-year contract. Zubrus is a 16-year NHL veteran, who has spent the past six seasons with the Devils.
Zubrus had two goals and seven assists in 22 games last season. He missed 26 games after having surgery to repair an injured left wrist.
New Jersey is expected to lose forward David Clarkson, who will test free agency on Friday. Forwards Steve Sullivan, Alexei Ponikarovsky and defenseman Marek Zidlicky are also eligible to become unrestricted free agents.
The Devils made another move Thursday, placing veteran backup goalie Johan Hedberg on unconditional waivers. That makes Hedberg eligible to have the remaining year of his contract bought out.
Hedberg is a 12-year NHL veteran who has become the odd-man out in New Jersey. Longtime starter Martin Brodeur has one year left on his contract, and the Devils made a move to secure his successor by acquiring goalie Cory Schneider in a trade with Vancouver during the NHL draft on Sunday.
Hedberg had a 6-10-3 record and one shutout last season. Overall, he has a 161-143-36 record with 22 shutouts.