Radek Dvorak played his junior hockey for MC Budejovice in the Czech Republic beginning in 1993-94 and went to play seasons with the team before making his North American and NHL debut in 1995-96.
After missing the 1995 World Junior Championships with an injury, Dvorak helped his country win gold at the Junior Four Nations Tournament in February 1995. He led the tournament with eight points in three games and was named the Best Forward.
Dvorak was selected tenth overall in the 1995 NHL Entry Draft by the Florida Panthers and made his NHL debut that season while still just 18-years of age, helping the Panthers improve 46 points and make the playoffs for the first time in franchise history. In the playoffs, the Panthers won the Prince of Wales Trophy before losing in the Stanley Cup finals to the Colorado Avalanche.
By 1998-99, Dvorak was up to 43 points and had a team-high four short-handed goals. In 1999-2000, he joined the New York Rangers after 35 games with the Panthers in a three-team deal that also involved the San Jose Sharks. He finished the season with 18 goals and 50 points. In 2000-01, Dvorak played all 82 games with the Rangers and scored 67 points, good enough for fourth on the team.
In 2001-02 Dvorak's point total dipped and he was subsequently dealt to the Edmonton Oilers at the trading deadline in March of 2003. Upon his arrival with the Oilers, Dvorak has been one of the teams most productive forwards.
In the 2005-06 playoffs Dvorak would sit out of a hand full of games due to injury before returing to the Oiler lineup for the playoffs. The Oilers would lose in seven hard fought games to the Carolina Hurricanes, and Dvorak would sign with the St. Louis Blues in the off-season.
In St. Louis, Dvorak competed in all 82 games of the 2006-07 NHL regular season, recording 10 goals and 27 assist on a struggling Blues team. Dvorak's stint in St. Louis last only one season after the Florida Panthers signed him as a free agent in the summer of 2007.
In Florida, Dvorak would put up solid if unspectacular offensive numbers, including seasons of 15 and 14 goals respectively, but his time with the Panthers would come to an end at the 2011 NHL trade deadline. He was sent to the Atlanta Thrashers in exchange for Patrick Rissmiller and Niclas Bergfors.
On July 1, 2011, Dvorak was on the move again. This time as an unrestricted free agent he signed a deal with the Dallas Stars.
Entering the 2012-13 NHL season, Dvorak was an unrestricted free-agent. On March 24, 2013, he reached an agreement with the Anaheim Ducks.