The Wild (42-24-9) are third in the Central Division, three points ahead of the Colorado Avalanche and 14 behind the first-place Predators.
"We could use a few more big bodies getting to the front of the net," Minnesota general manager Chuck Fletcher said. "There's not a lot of pretty goals this time of year. You have to get [to the net], you have to take the goalie's eyes away, you have to fight for space, and Jordan does a good job of that."
Greenway (6-foot-6, 226 pounds) will wear No. 18 and meet the Wild in Nashville on Monday.
"In a perfect world, you'd love to [get Greenway] a practice," Minnesota coach Bruce Boudreau said. "But it's not going to take long to get him involved in everything."
Fletcher said Greenway can provide energy to the Wild, who are on track to clinch a berth in the Stanley Cup Playoffs for a sixth consecutive season.
"It's rare to find a player with that combination of size, speed and skill, and he's a guy that we think is ready to play in the NHL," Fletcher said. "I certainly think he can fit in our top 12 to play, and it'll be up to Bruce and the coaches to find the right role and obviously it'll be important for Jordan to show well too and play well.
"I think his game's defined by more than just offense, the puck protection, the ability to play defensively, to win battles along the wall, he brings a lot of elements to the game that are really important."
Greenway spent the past three seasons at Boston University, where he had 92 points (28 goals, 64 assists) in 112 games. He had 35 points (13 goals, 22 assists) in 36 games during his junior season to help Boston University win the 2018 Hockey East tournament and advance to the NCAA Northeast Regional Final, when it lost to Michigan 6-3 on Sunday.
Greenway played center in college, but Fletcher said he will likely be moved to wing.
"Maybe he's defense, you never know," Boudreau joked. "He's played everywhere for BU this year."
The Wild were especially impressed with Greenway's performance at the 2018 PyeongChang Olympics, when he scored one goal in five games for the United States. He also won gold medals playing for the U.S. at the 2017 IIHF World Junior Championship and 2015 Under-18 championship.
"This is a big talent, a talented kid," Boudreau said. "He's not like a 19-year-old kid that's 170 pounds and still got 15-20 pounds to put on. He's a man … so he's going to be able to compete with the men once he gets his legs underneath him.
"We'll see. We want to give him the opportunity to help our team win."
