The 24-year-old Russian led all rookies in goals (30), assists (47), points (77), power-play goals (eight), power-play points (24) and game-winning goals (7) in 80 games in 2015-16.
Panarin is the first Chicago player to win the award since Patrick Kane in 2007-08.
Also nominated at the NHL Awards in Las Vegas were Edmonton Oilers forward Connor McDavid and Philadelphia Flyers defenceman Shayne Gostisbehere.
The top pick at the 2015 draft, McDavid finished fourth in rookie scoring with 16 goals and 32 assists despite appearing in just 45 games due to injury.
Gostisbehere led rookie defencemen in goals (17), assists (29), points (46), power-play goals (eight), power-play points (22) and game-winning goals (five) in 64 games.