Norelius was born in Stockholm, Sweden in 1909. Her father was Swedish Olympic swimmer Charles Norelius, who was also her swimming coach. She was first recognized for her swimming and diving skills just after her seventh birthday, at an exhibition at the Greenbrier pool, where her father was a swimming instructor.
At the age of 15, she represented the United States at the 1924 Summer Olympics in Paris. She remains the only woman to have received two Olympic back-to-back gold medals in the 400-meter freestyle. Norelius died in 1955, following gall bladder surgery and was buried in Bellefontaine Cemetery.
She was inducted into the International Swimming Hall of Fame as an "honor swimmer" in 1967.
Norelius won the gold medal in the women"s 400-meter freestyle in 1924, setting a new Olympic record (6:022), and edging fellow Americans Helen Wainwright (6:038) and Gertrude Ederle (6:048). Four years later, at the 1928 Summer Olympics in Amsterdam, she won two more gold medals. First, in individual competition, she won the women"s 400-meter freestyle, breaking her own record with a new world mark of 5:42.8, and defeating Dutch swimmer Marie Braun by fifteen seconds. In the women"s 4×100-meter freestyle relay event, Norelius and her American teammates Eleanor Garatti, Adelaide Lambert and Albina Osipowich, won the gold medal and set a new world record in both the event final (4:476). Between 1925 and 1929, Norelius won eleven individual Amateur Athletic Union (Amateur Athletic Union) titles and set at least 19 world and 30 American records. In 1929 she turned professional and won the ten-mile Wrigley Marathon in Toronto.
