Union College forward Mike Vecchione and Northeastern forward Zach Aston-Reese were the other finalists.
Butcher, whose NHL rights are held by the Colorado Avalanche, is the first defenseman to win the award since Matt Gilroy of Boston University in 2009, and sixth in history.
Butcher had 37 points (seven goals, 30 assists) in 42 games this season, and his plus-27 rating ranks ninth in the nation.
The 22-year-old was named National Collegiate Hockey Conference player of the year and offensive defenseman of the year, helping Denver win the NCHC regular-season championship. Butcher and defenseman Matt Carle (2006) are the only players from Denver to win the award.
Butcher is captain at Denver, which will play Minnesota-Duluth for the national championship on Saturday. He had an assist in a 6-1 semifinal win against Notre Dame on Thursday.
"I think myself and my teammates and the coaching staff at DU realized it right after we lost to North Dakota last year in the Frozen Four," Butcher said. "Just that game and the offseason, just working towards where we are now, it's been a great ride, but we're not done yet."
Butcher was a fifth-round pick (No. 123) by Colorado in the 2013 NHL Draft.
Vecchione, 24, who signed with the Philadelphia Flyers on March 31 and made his NHL debut April 4, tied for the NCAA lead with 63 points (29 goals, 34 assists) in 38 games.
Aston-Reese, 22, tied with Vecchione for the scoring lead with (31 goals, 32 assists) in 38 games and signed with the Pittsburgh Penguins on March 14.
Jimmy Vesey (Harvard) of the New York Rangers won the award last year. Jack Eichel (Boston University) of the Buffalo Sabres won it in 2015, and Johnny Gaudreau (Boston College) of the Calgary Flames won it in 2014.