The contract was agreed to last week, subject to a physical, and the team said Wright planned to discuss it Wednesday at the winter meetings.
"I've grown up in this organization and made lifelong friendships with teammates, uniform personnel and front office staff. I'm grateful for the opportunity to finish what I've started," Wright said.
Wright's new deal replaces the $16 million salary he was to have earned under a 2013 option in his previous contract. The new deal contains deferred money.
"We're thrilled for the organization and our fans that David will be a Met for many years to come," Mets chief operating officer Jeff Wilpon said. "As great a player as David's been with us on the field - one of the greatest and most popular Mets ever - he's been equally outstanding in the community."
Without the agreement, Wright could have become a free agent after the 2013 season. New York also is trying to reach a new deal with NL Cy Young Award winner R.A. Dickey, who is signed for $5.25 million next year and then can become a free agent.
Mets general manager Sandy Alderson spoke briefly Monday with Dickey's agent, Bo McKinnis.
"I don't think we've reached the point where there isn't something possible, but time will tell," Alderson said. "I think we've always said we'd like to sign R.A. and keep him in New York."
Alderson has been exploring trade possibilities involving Dickey.
"Something could happen on either front that would bring this to a conclusion, presumably," Alderson said. "I don't expect that's going to happen today. It may not happen tomorrow. It may not happen in Nashville."
Wright, who turns 30 on Dec. 20, batted .306 with 21 homers and 93 RBIs last season as the Mets went 74-88 and finished fourth in the NL East for the fourth straight year. He also had a .391 on-base percentage to go with 41 doubles and 15 stolen bases.
Teammate Johan Santana signed a $137.5 million, six-year contract with New York after being acquired in a trade from Minnesota before the 2008 season.
Selected with the 38th overall pick in the 2001 amateur draft, Wright made his Mets debut in July 2004 and quickly secured the job at third base - a trouble spot for the team throughout its colorful history.
Wright has made six All-Star teams and won two Gold Gloves, compiling a .301 career average with 204 home runs and 818 RBIs in 8 1/2 major league seasons. He is the club's career leader in several major offensive categories including hits, RBIs, runs and walks.
"I think it's a great statement that David wanted to stay with the organization that drafted him," Mets manager Terry Collins said. "David is the leader of this team in the clubhouse, on the field and in the community."
New York has lowered its payroll in recent seasons as attendance has declined at Citi Field. Asked whether next year's budget was based on the same home attendance as this year, 2.2 million, Alderson said the revenue projection was produced by another department. Then he added: "Well, I don't think it's predicated on 4 million."