Šatan was drafted in the fifth round of the 1993 NHL Entry Draft (111th overall) by the Edmonton Oilers, for which he spent the better part of 2 seasons. He was traded to the Buffalo Sabres in the 1995-1996 season. Šatan enjoyed his best two seasons with the Sabres, the first in 2001-2002 (37 goals, 36 assists, 73 points), and then in 2002-2003 (26 goals, 49 assists, 75 points).
Islanders and after
Šatan became a free agent after the lockout season of 2004-2005 and signed a contract with the New York Islanders. After his three-year contract expired prior to the start of the 2007-2008 season, he was signed by Pittsburgh. He is curretly playing for the teams minor-league affiliate.