Greene gets a four-year contract, his agent, Dan Plante, confirmed to ESPNNewYork.com. The deal has an average annual value of $3 million, according to the Bergen Record.
"I got some phone calls from other teams, but we were in the process of wrapping things up with New Jersey (around noon)," said Plante, who declined to divulge the average annual value of the pact. "I never talked financial aspects with anyone else. As Andy said all along, he wanted to be back in New Jersey."
Greene, 28, played in all 82 games for the Devils last season, with four goals and 19 assists.
General manager Lou Lamoriello called Greene one of the Devils' top four defenseman. He played in all 82 games last season, collecting four goals and 19 assists.
However, Greene had a minus-23 rating, meaning opposing teams scored 23 more times than the Devils did when he was on the ice. Entering his sixth NHL season, Greene has 15 goals and 70 assists in 291 career regular-season games.
"I don't think," Lamoriello said, "last year was indicative of the years he has played for us."
Lamoriello had hoped to get Greene's deal completed before free agency started at noon on Friday.
"Until it's done you are always concerned," Lamoriello said. "That's with everything you do."
Hedberg went 15-12-2 with a career-best 2.38 goals-against average, a .912 save percentage and three shutouts.
"New Jersey was my first choice," Hedberg told the Record.
"There was interest (from other teams), which is great. It's flattering, but with everything accounted for, I felt good about coming back here."
"Hedberg, what he did for us -- both on the ice and off the ice -- speaks for itself," Lamoriello said.
Hedberg has a career mark of 138-126-31 with 17 shutouts and 2.88 goals-against average in 327 games over nine seasons with Pittsburgh, Vancouver, Dallas, Atlanta, and New Jersey.
Mike Mazzeo is a frequent contributor to ESPNNewYork.com. Information from The Associated Press was used in this report.