In 1956 Vilhjálmur set a new Olympic Record by jumping 16.26 m in the triple jump, only to be surpassed by Brazil's Adhemar da Silva in the same competition. This was the most unexpected result of the Olympics that year, and his silver medal was Iceland's first ever Olympic medal. In 1958 he took bronze in the triple jump at the European Athletics Championships in Stockholm, Sweden, with 16.00 m. His personal best was 16.70 m set in 1960 in Laugardalsvöllur, Iceland. He was named Icelandic Sportsperson of the Year five times, more times than anyone else.