[1] During his tenure within the Oilers organization, Wells played between minor-league affiliates, the Bakersfield Condors of the AHL and the Wichita Thunder of the ECHL.

As a free agent from the Wolves, Wells opted to continue his professional career in the AHL after agreeing to a one-year contract with the Rockford IceHogs on July 14, 2022.

[4] Beginning the 2022–23 season with the IceHogs, Wells was signed to a one-year NHL contract by the Chicago Blackhawks on November 5, 2022, due to a rash of injuries.

[5][6] Serving as the Blackhawks' backup goaltender he surprisingly made his NHL debut, called into the game in a relief appearance against the Winnipeg Jets on November 5, 2022.

On March 2, 2023, the Blackhawks traded Wells along with Max Domi to the Dallas Stars in exchange for Anton Khudobin and a second-round pick in the 2025 NHL Entry Draft.