Selivanov never played for Philadelphia, however, and made his NHL debut with the Tampa Bay Lightning, for whom he played parts of five seasons. He was later dealt to the Edmonton Oilers. During the 1999–2000 season, Selivanov briefly led the league in scoring, before injuries and a prolonged slump stopped him. He finished the season with 27 goals. After one more season, a disappointing one with the Columbus Blue Jackets, Selivanov returned to Europe, playing in Russia and Germany. In January 2008 was announced that he changes from Germany to Switzerland to play with Fribourg Gotteron in the national league A.
Selivanov's father-in-law is Hockey Hall of Famer Phil Esposito.