Sandlak, 20, leads the Plymouth Whalers of the Ontario Hockey League with 16 goals and 24 points in 26 games.
"Carter is a gritty, tough competitor who is having a good year for Plymouth in the Ontario Hockey League," Hurricanes vice president of hockey operations Ron Francis said in a statement announcing the signing. "He's got an edge to his game and the work ethic to be a good pro."
The contract will pay Sandlak $550,000 at the NHL level in the first two seasons and $575,000 in the third season. He also will make $55,000 if he's in the American Hockey League in the first season, and $67,500 if he's in the AHL the second and third seasons. He also will receive a $110,000 signing bonus.