Drafted in 1988 by St. Louis, the smooth skating Hedican went on to play three years of college hockey at St. Cloud State. In 1990-91, he played 41 games for the Huskies, notching 21 goals and 26 assists to earn on spot on the WCHA First All-Star team. The 1991-92 season was a busy one for Hedican: he represented his country on the National Team and the U.S. Olympic team in Albertville, France. He then made his first NHL appearance with the Blues in March, and just a few weeks later he scored his first NHL goal.
Hedican split the 1992-93 season between the Blues and the Peoria Rivermen of the IHL. From 1993-94 onward, it has been all NHL for Hedican, including two World Championship tournaments. He started the 1993-94 season in St. Louis, playing 61 games there before being traded to Vancouver in March 1994 as part of a multi-player deal. He had a steady job with the Canucks for the next four years, missing the occasional game due to injuries and consistently tallying double-digit point totals. His career best season was 1995-96, when he combines six goals and 23 assists for 29 points in 77 games.
Hedican remained with the Canucks until January 1999 when he was traded to the Florida Panthers in a deal involving players and draft choices. He had a 25-point season with the Panthers in 1999-00, the year in which he played his 500th NHL game.
After parts of four seasons with the Panthers, Hedican was dealt to the Carolina Hurricanes where he was a key player in the team's run to the 2002 Stanley Cup Final before falling to the Detroit Red Wings.
After two steady seasons with the Hurricanes the defenceman did not play during the lockout of 2004-05. Hedican returned to competition in the 2005-06 season where he would tie his career high 27 point total in the regular season. In April of 2006, Hedican was named Carolina's nominee for the Bill Masteron Trophy following his return from a pair of knee surgeries and back surgery to enjoy a resilient season with the Hurricanes. Throughout the Hurricanes run to the finals Hedican was a regular on defense appearing in all 25 games as he and the team captured their first ever Stanley Cup.
On an international level, Hedican represented the United States of America in the 2006 Olympic Games in Turin.