Yagudin began competing internationally in 1994 and won the World Junior Figure Skating Championships in 1996. He was coached by Alexei Mishin from approximately age 12 to 18. In 1999, Yagudin relocated to the United States to train with Tatiana Tarasova, who continued to coach him until his retirement in 2003.
Yagudin won his first major title at the 1998 European Figure Skating Championships. One month later he placed fifth at the 1998 Winter Olympics in Nagano, Japan. He went on to win the 1998 World Figure Skating Championships.
Yagudin continued his success in the 1998-99 season, winning the Grand Prix Final, European Championships and World Championships.
Yagudin struggled early in the 1999-2000 season but came back to win the World title.
In 2001-02, he won every event he entered, including the Olympic Games in Salt Lake City, Utah. He was the first male skater in 50 years to earn the first-place votes of every judge in all stages of the competition. He was given four 6.0s for presentation; no other man had ever scored more than one perfect mark in the history of the Olympic Games.
At the World Figure Skating Championships in Japan in 2002, he became the first skater to receive six 6.0s for presentation and the first to receive a 6.0 for required elements.
A congenital hip disorder forced him to retire from eligible competition in 2003. Yagudin then turned professional, touring with Stars on Ice and Ice Symphony in Russia.