He is a four-time World's Strongest Man, having won in 1991, 1994, 1995, 1996 and is widely regarded as one of the greatest strongmen of all time.

Magnús competed in his first strongman contest in 1985, finishing third in the Iceland's Strongest Man competition won by Jón Páll Sigmarsson.

He decided to focus solely on strongman competition after he won the 1991 World's Strongest Man contest.

He competed in a one-off event at the Giants Live Strongman Championship 2019 held in Wembley against fellow strongman legend Bill Kazmaier in the Hercules Hold, with the weight being reduced by 20 kg on each side from what the professional athletes were working with.

He also appeared in a Coors Light commercial as the "World's Strongest Man" which aired in the U.S. Magnús frequently judges international powerlifting and strongman competitions.