The deal will pay Welsh $700,000 on the NHL level or $105,000 at the minor-league level this season. In 2013-14, Welsh will receive $1 million.
"Jeremy is a player we think very highly of," general manager Jim Rutherford said in a statement. "He is a big man (6-foot-3, 200 pounds) that can play center or left wing, and has really good hockey sense."
Welsh, 23, made his NHL debut for the Hurricanes in the team’s final game of the 2011-12 season. He had 27 goals, 17 assists and 47 penalty minutes in 40 games for Union College last season, ranking first on the team and fourth in the NCAA in goals (27).
Union College reached the Frozen Four, where it lost to eventual runner-up Ferris State.