The U.S. Basketball Writers Association presented the trophy at its annual college basketball awards breakfast in San Antonio.
Hansbrough has led the Tar Heels to 36 wins going into their game against Kansas in the NCAA Tournament semifinals Saturday.
Hansbrough.of Poplar Bluff, Mo., was named the top college freshman player by the basketball writers two years ago.
The North Carolina forward, who has averaged more than 23 points and 10 rebounds per game, was named Atlantic Coast Conference player-of-the-year this season.
Robertson, a member of basketball's Hall of Fame, was an all-America college player and all-star in the NBA. In 1996, he was named one of the 50 greatest players in NBA history.