Minaya said that he had been in talks with Greenberg since Sunday about working out a deal for the All-Star shortstop.
Reyes would have been eligible for arbitration at the end of this season, but the new deal ensures that he will remain a Met for the next several years.
"I'm really happy to have the opportunity to be here for a long time," Reyes said. "I'm just going to keep playing hard and hope to get to the World Series and win a championship."
Reyes, who will now earn $2.5 million in 2007, has been with the Mets since the age of 16. He had made it clear to the organization that he wanted to remain in New York.
"It's great for me and my family to be playing in New York for a long time," Reyes said. "It's exciting for me. I know now I'm going to be here for a long time and I don't have to worry."
Reyes missed a large part of the 2004 season due to a stress fracture of the left fibula and a strained right hamstring, but he said that the fear of hurting himself didn't play into his desire for more job security.
"I don't worry about injuries anymore. That's way behind me," Reyes said. "I just do my job."
Mets manager Willie Randolph said the move shows the club's faith in Reyes' ability and his potential for the future.
"I think it's great for Mets fans to be able to watch him play," Randolph said. "He's only scratching the surface of what he can do. Not just with his speed, but power-wise. He's going to fill out and get stronger. The ceiling is real high."
The Dominican-born Reyes was signed by the Mets to a non-draftee free-agent contract in 1999, and he spent three years in the club's Minor League system. Reyes made his debut with the Mets in 2003, finishing second among Major League rookies in batting and stolen bases.
He played just 53 games in an injury-plagued '04 season, but he bounced back with a breakout campaign in 2005, in which he led the National League in triples and stolen bases. Reyes already is fifth on the Mets' all-time stolen-base list with 136.
The shortstop has continued his outstanding play this season, leading the Majors in triples (13) and stolen bases (44). He's also second with 88 runs scored and has tied a franchise record for home runs by a shortstop with 10.
He was rewarded for his first-half efforts with a starting spot on the National League All-Star team, but he was unable to play due to injury.