The 24-year-old Hellberg appeared in 38 games with the Milwaukee Admirals of the AHL last season, posting a 15-10-6 record along with a 2.33 goals-against average.
Hellberg also represented the Western Conference at the recent AHL All-Star Game.
The native of Uppsala, Sweden, was acquired from Nashville on July 1 in exchange for a sixth-round pick in the 2017 draft.
Hellberg was originally selected by the Predators in the second round of the 2011 draft and appeared in one NHL game in 2013.
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