He began his ballet training in Reykjavik with a local teacher and went on to join the National Theatre’s affiliated school, which at the time was led by Erik and Lisa Bidsted.
Tomasson's professional dance career started at age 15 with the Pantomime Theatre in Copenhagen’s Tivoli Gardens.
At age 17, he was discovered in his homeland by choreographer Jerome Robbins, who arranged a scholarship for Tomasson to study at the School of American Ballet' in New York City.
Of this time, Helgi recalls "Living for so long in New York, I grew up with the best, and I was a part of that time.”[4] The company's founding balletmasters George Balanchine and Jerome Robbins both created roles expressly for Tomasson.
Balanchine created a solo for him in Divertimento from Le Baiser de la Fée for the 1972 Stravinsky Festival.
When reviewing this last performance, the New York Times wrote, “With his outstanding technique and elegance, Mr. Tomasson was the epitome of the classical male dancer.
During his time with the company, he staged many full-length ballets, including Swan Lake in 1988, The Sleeping Beauty in 1990, Romeo and Juliet in 1994, Giselle in 1999, Don Quixote (in collaboration with principal dancer Yuri Possokhov) in 2003, and Nutcracker in 2004.