Igor he made his ballet debut in Paris in 1932. He remained in Paris and continued his studies with Olga Preobrajenska for the next two years. In 1934 Youskevitch joined Bronislava Nijinska's Les Ballets de Paris, and in 1935 he became a member of Leon Woicikowski's ballet. Colonel de Basil sponsored Woicikowski's tour of Australia starring Igor Youskevitch and André Eglevsky in 1937. While with the Woicikowski's Ballet ,Youskevitch met Anna Scarpova, a dancer with the company, and they were married in 1938. That same year, Youskevitch and Scarpova became members of the Ballet Russe de Monte Carlo. He remained there until he volunteered to served in the U.S. Navy in 1944.
In 1946, he joined Leonide Massine's Ballet Russe Highlights, and that fall he became a premier danseur of Ballet Theatre, now American Ballet Theatre. While with ABT he and Alicia Alonso (created roles in George Balanchine's Theme and Variations in 1947. As a team they became world renowned, and in 1948 he was guest artist with Alonso's Cuban Ballet. Youskevitch created a role in Antony Tudor's Shadow of the Wind in 1948 and he danced in Gene Kelly's movie Invitation to the Dance in 1952.
After leaving ABT in 1955, Igor returned with Alonso to star for Ballet Russe de Monte Carlo. Igor Youskevitch won the Dance Magazine Award in 1958, In 1960 he rejoined Ballet Theatre as a Guest Artist on their first visit to the Soviet Union.
He retired from the stage in 1962, but not from dance. Youskevitch was on the faculty of the University of Texas in Austin from 1971 to 1982. He co-founded the New York International Ballet Competition in 1985, and he remained its Artistic Director until his death. He was awarded the Capezio Dance Award in 1991 and passed away in 1994.