The deal will pay Dvorak US$600,000 on the NHL level or $125,000 on the American Hockey League level, with a guarantee of at least $250,000 for the 2013-14 season.
Dvorak, 36, split the 2012-13 season between HC Davos of the Swiss league and the Anaheim Ducks in the NHL, totalling seven points in seven games for Davos, and four goals in nine games with the Ducks.
Originally selected by the Florida Panthers with the 10th overall pick of the 1995 draft, Dvorak has appeared in 1,200 NHL games with Florida, the New York Rangers, Edmonton, St. Louis, Atlanta, Dallas and Anaheim.
The Tabor, Czech Republic, native has totalled 223 goals, 358 assists and 408 penalty minutes in regular-season NHL action, and added two goals and five assists in 39 Stanley Cup playoff games.
"Radek is an veteran player, and he has shown us throughout training camp that he can contribute to the Hurricanes," Hurricanes general manager Jim Rutherford said in a statement. "His versatility and experience give our coaching staff a number of options with our lineup."
The six-foot-two, 195-pound forward ranks eighth among active NHL players in games played, and competed for the Czech Republic at the 2002 Winter Olympics, the 1999, 2001, 2004 and 2005 IIHF World Championships and the 2004 World Cup of Hockey.