Eklund's parents were actors, but he initially decided not to follow in their footsteps and went to trade school. Around the age of nineteen, he was on a tour with his parents, where he made his stage debut. He subsequently began taking private acting lessons. He got a job at Helsingborgs city theater. In the 1950s, he was employed at Malmö theater, which was managed by Ingmar Bergman. Since then, he has performed with different theater troupes around Sweden.