He also spent five years in the National Hockey League (NHL), playing for the New York Islanders, Pittsburgh Penguins, Edmonton Oilers, and Columbus Blue Jackets.

In January 2013, while playing for AIK, Tärnström was forced to retire due to a spinal disc herniation injury.

Tärnström requested a trade from the Pittsburgh Penguins and on January 26, 2006, he went to the Edmonton Oilers in exchange for Cory Cross and Jani Rita.

Tärnström was part of the Cinderella Edmonton Oilers team that made a run to the Stanley Cup Finals.

AIK were promoted to the SEL in the 2009–10 season, and Tärnström would remain in the team until he was forced to retire in January 2013 due to a spinal disc herniation injury.