Evensson was born in Torsby and his family moved from Torsby to Hagfors when Conny was just two years old. He started his hockey career with Hagfors club IK Viking before signing with Malmö FF in 1965.
Conny Evensson's early life involved moving from Torsby to Hagfors when he was just two years old. He started playing hockey for the local club IK Viking before eventually signing with Malmö FF in 1965.