Sami began his professional career with TPS of the Liiga before being selected by the Ottawa Senators with their last pick in the 1996 NHL Entry Draft. He joined the Senators in 1998-99 and was selected to the NHL All-Rookie Team. In the 2002 off-season, Ottawa traded Sami to the Vancouver Canucks. While playing for the Canucks, Sami recorded three 30-point seasons. Prior to the 2012-13 season Sami signed with the Lightning as a free agent.
Internationally, Sami played for Team Finland, appearing in two World Championships, three Winter Olympics and one World Cup. He won silver medals at the 2001 World Championships and the 2006 Winter Olympics, as well as a bronze medal at the 2010 Winter Olympics.
Throughout his career, Sami fought through countless injuries. Despite his injuries, he will be remembered as a two-way defenceman with a powerful slapshot and a knack for scoring power-play goals.