The Capitals made the deal in hopes of improving their American Hockey League team, the Hershey Bears. The 11-time Calder Cup champions are ninth in the Eastern Conference and have gone 4-4-1-1 in their past 10 games.
"Hershey isn't playing the way we would like them to play; we have had really good teams there for a number of years and we are just trying to shake things up a little bit," Capitals general manager George McPhee said Thursday before the Capitals played the Toronto Maple Leafs.
"They are similar players and we are just hoping that a change for both players will help Hershey."
Wellman has played in 41 NHL games, with four goals and nine assists, all for the Minnesota Wild. He has 23 points in 37 games this season with the Panthers' AHL affiliate, the San Antonio Rampage.
Though the 25-year-old has been acquired to give the Bears a shot in the arm, joining the Capitals at some point is always a possibility.
"We have a full roster here, but he is capable if he is playing well, and if we have some injuries, he would be a good call up," McPhee said. "Hopefully (the deal) is good for them and good for both teams."
Hamill, 24, has 20 games of NHL experience with the Boston Bruins over three seasons. He had 22 points in 40 games for Hershey this season.
In addition to Wellman, the Capitals also acquired forward Peter LeBlanc from the Chicago Blackhawks in exchange for future considerations Thursday.