Butcher, 22, became a free agent after not signing with the Colorado Avalanche, who selected him in the fifth round (No. 123) of the 2013 NHL Draft.
"We are immensely excited to have Will and his family join our organization," New Jersey general manager Ray Shero told Northjersey.com. "This continues to represent what we want to do as a team: Bring in talented individuals, invest in their talent, and develop them as we progress."
Butcher reportedly also considered the Buffalo Sabres, Los Angeles Kings and Vegas Golden Knights.
"It was a difficult decision for Will because a number of teams did a great job of presenting how they could help Will grow into an NHL player," agent Brian Bartlett said. "Ultimately, Will and his family felt like New Jersey provided a good mix of opportunity, coaching, development, style of play, and returning players. Will has always been an offensive defenseman and felt like if he continues to develop, there could be a chance to help on New Jersey's power play in the future."
Butcher won the Hobey Baker Award as the top player in NCAA Division I men's hockey last season. He had 37 points (seven goals, 30 assists) in 43 games for the University of Denver, which won the NCAA championship.