Hellkvist has written a two-year contract with Växjö and succeeds Jörgen Jönsson, who was presented as the new coach in Färjestad on Monday.
Hellkvist coached Björklöven in HockeyAllsvenskan last season, but was fired at the end of February.
The 48-year-old coach was on loan to Björklöven from Leksand, where he did not get renewed confidence after a longer period of sick leave.
Hellkvist has also been the head coach for Malmö in SHL and Rögle, Oskarshamn, and Modo in HockeyAllsvenskan.
"First and foremost, I feel very proud and happy to represent such a fine club that has shown good results in recent years. Växjö has always been tough to beat when you've come here as an opponent, and if you can't beat them, 'join them'," says Hellkvist.
Växjö has won four Swedish Championship titles since 2015, the latest in 2023, but was eliminated in the quarterfinals against Luleå this season.