Born in Hallein, Veith is from the village of Adnet in Salzburg and made her World Cup debut at age 17 in November 2006. She competed in all five alpine disciplines, but omitted slalom as of January 2012. Her first major success was becoming world champion in the super combined in 2011, without having won a World Cup race before. At the 2014 Winter Olympics in Sochi, Russia, Veith won the super-G at Rosa Khutor for her first Olympic medal, and at the end of the season she won the World Cup overall and giant slalom titles.