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 and holds team 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 Elias has topped 70 points in a season five times. That includes the 2011-12 season when he had 78 points (26 goals, 52 assists) in 81 games.
New Jersey also re-signed veteran forward Dainius Zubrus to a three-year, $9.3 million contract. A person familiar with the deal revealed the terms to The Associated Press on the condition of anonymity because the Devils didn't release those numbers.
Zubrus is a 16-year NHL veteran, who has spent the past six seasons with New Jersey.
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 defenceman Marek Zidlicky are also eligible to become unrestricted free agents.
The person also revealed the Devils placed veteran backup goalie Johan Hedberg on unconditional waivers for the purpose of buying out the final year of his contract.
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 went 6-10-3 with one shutout last season. Overall, he is 161-143-36 with 22 shutouts.