Sotomayor set the junior world record in 1984 by clearing 2.33 metres in Havana, but was not able to go to the 1984 Olympics due to the Cuban boycott.

In 1985 he took silver in the World Indoor Championships with a best jump of 2.30 metres, and won his first title in 1987, at the Pan American Games. The following year at Salamanca he set a world record of 2.43 metres, but was denied the chance to compete at the 1988 Olympics due to another Cuban boycott.

He twice increased the world record, to 2.44 metres (8 ft 0.06 in) on July 29, 1989 in San Juan and to the current record of 2.45 metres (8 ft 0.46 in) on July 23, 1993 in Salamanca. Sotomayor also set the current world indoor record of 2.43 metres (7 ft 11.67 in) on March 4, 1989 in Budapest.

When he was finally able to compete in the Olympics he won the gold medal at the 1992 Olympics and the silver medal at the 2000 Olympics (after the reversal of a drug suspension for drug usage). Between the games he won the 1993 and 1997 World Championship.

Sotomayor has a rare dominance in the history of this event. Of the 24 all-time best high jumps, 17 are his; he has cleared 2.40 meters more times than any other athlete and is the only person to have cleared 2.44 m (8 ft). The last time he cleared 2.40 meters was on March 25, 1995 at the Pan American Games in Mar del Plata, Argentina. No one has jumped higher since. It was only equaled by Vyacheslav Voronin in London in August 2000, Stefan Holm in Madrid in 2005 and Ivan Ukhov in Piraeus in April 2009.