A first-round pick (18th overall) in the 2012 MLB Draft, the 22-year-old Seager was unanimously selected for the honor by the Baseball Writers' Association of America.
Seager hit .308 with 26 home runs, 72 RBIs and 105 runs scored in 157 games this season. In two postseason series, he batted .205 (9-for-44) with two home runs and four RBIs.
His 72 RBIs led all rookies in the majors, and he ranked first among qualifying first-year players with a 6.1 wins above replacement rating.
Seager was named an All-Star and also won the Silver Slugger Award.
He joins retired shortstop Nomar Garciaparra as the only rookie shortstops in major league history to hit at least 25 homers and score 100 runs, according to ESPN.
Fulmer, 23, posted an 11-7 record with a 3.06 ERA and 132 strikeouts over 159 innings in 26 starts in 2016.
A first-round pick (44th overall) of the Mets in the 2011 draft, Fulmer was traded to Detroit in the July 31, 2015, deal that sent star outfielder Yoenis Cespedes to New York.
Fulmer led all AL rookie pitchers in wins and innings pitched.
Los Angeles Dodgers pitcher Kenta Maeda and Washington Nationals outfielder Trea Turner joined Seager as finalists for the NL award, while Cleveland Indians outfielder Tyler Naquin and New York Yankees catcher Gary Sanchez were the other AL finalists.