Gaudette was selected by the Vancouver Canucks in the fifth round (No. 149) of the 2015 NHL Draft after he had 30 points (13 goals, 17 assists) in 50 games for Cedar Rapids of the United States Hockey League.
Gaudette played the next three seasons at Northeastern University, where he had 142 points (68 goals, 74 assists) in 116 games. As a junior in 2017-18, he led the nation in points (60) and points per game (1.62) and became the first player from Northeastern to win the Hobey Baker Award as the best player in NCAA Division I hockey. Gaudette also won the Hockey East Player of the Year, was named to the America Hockey Coaches Association East First-Team All-American, and ended his collegiate career as Northeastern's all-time leader in power-player goals (32).