The 24-year-old forward, who could have become a restricted free agent after this season, has scored 13 points (four goals, nine assists) in 33 games, including 10 (four goals, six assists) in his past 16.
"Jordan's play over the last couple months has really been great," Wild general manager Bill Guerin said. "The way he's been a big part of that line with [Joel] Eriksson Ek and [Marcus] Foligno is something that we want to keep around.
"And we've seen a growth in Jordan over the last couple years that we feel will continue and Jordan will keep getting better and better. This is a place he's expressed that he's comfortable, he wants to be here, he believes in what he's doing. And we believe in Jordan and the direction that he's going. We are extremely happy to have him back for three more years."
Selected by the Wild in the second round (No. 50) of the 2015 NHL Draft, Greenway has scored 98 points (30 goals, 68 assists) in 243 regular-season games and five points (two goals, three assists) in 16 Stanley Cup Playoff games.
However, Guerin said the desire to keep Greenway had to do with more than numbers.
"He's got offensive capabilities, but just as important Jordan has intangibles that he brings to the table," Guerin said. "Obviously his size (6-foot-6, 231 pounds), his speed, and his strength down low. He's got great vision. And personality-wise Jordan brings something to the dressing room that nobody else brings and that's just his personality. And the guys really love him, and he fits really well here and that's important. The chemistry of the team is extremely important, and Jordan is a big part of that."
The Wild (27-10-3), who have won five in a row, are third in the Central Division.
NHL.com independent correspondent Jessi Pierce contributed to this report
