Magnús competed in his first strongman contest in 1985, finishing third in the Iceland's Strongest Man competition won by Jón Páll Sigmarsson.
His strongman victories include the 1989 Pure Strength contest in Scotland, the 1991 and 1993 International Power Challenge, the 1992 Scandinavian Strongest Man (Finland), the 1992 Nordic Strongest Man (Denmark), the 1994 Europe's Strongest Man, the 1995 World Muscle Power Championship, and the 1995 and 1997 Viking Challenge.