Ekman was born in Stockholm, Sweden, and was the son of the director Hasse Ekman and Agneta (née Wrangel). Ekman represented the third generation in a family of prominent Swedish actors. First in the line was his paternal grandfather, also named Gösta Ekman, followed by his father Hasse Ekman, a successful film director and actor. Ekman's theatrical family also included his brothers Stefan Ekman and Mikael Ekman, a stage director, and his niece, Sanna Ekman, an actress. He was married from 1989 to artist and film director Marie-Louise Ekman, previously Marie-Louise De Geer Bergenstråhle, née Fuchs. Ekman sometimes appeared in credits as Gösta Ekman Jr. to avoid being confused with his famous grandfather.
