Magnús began powerlifting in 1984, and in 1985 he won a medal in the junior European and World Championships. He won the Senior European title in the 125 kg (276 lb) class in 1988 and 1990. His best lifts in competition include a 400 kg (882 lb) raw squat, 275 kg (605 lb) bench press with shirt and 250 kg raw bench press, 375 kg (827 lb) raw deadlift, and a raw total of 1015 kg (2238 lb). He once held the world record for a tire deadlift of 445 kg (981 lb).
In addition to his four World's Strongest Man titles, he was also runner-up in 1992 and 1993. He has also won the Iceland's strongest man competition many times and the West coast Viking (Vestfjarðavíkingurinn) of Iceland nine times, he is considered to be one of the first modern strongman competitors, and is regarded by many to be one of the best strongmen of all time. He carried Jón Páll's formula of being athletic for the dynamic tests of strength and having tremendous static strength to out lift some of the best Powerlifters. He was able to easily out deadlift the favoured O.D Wilson by 40 kg in 1991 and out squatted the world record holder in the squat, Gerrit Badenhorst, in 1995. After Magnus squatted 437.5 kg to parallel, Badenhorst commented that he had previously underestimated Magnus' pure strength and that Magnus' squat was the greatest squat he had ever seen from someone of his bodyweight.
Magnús lives with his fiancée Maggý Mýrdal, who is a company owner of a design store Fonts, her daughter Sóldögg María, and his daughter Vera, in Norðlingaholt, Iceland. His older daughter Maríanna lives in Akureyri and is studying nursing. Magnús frequently judges international powerlifting and strongman competitions.
Magnús owns a powerlifting and strongman gym in Reykjavík called Jakaból (giant's nest). The name Jakaból is a reference to an old gym in Reykjavík where Jón Páll Sigmarsson and many other Icelandic legends used to train.