Only three previous times have both leagues' Rookie of the Year been awarded unanimously: Benito Santiago and Mark McGwire in 1987, Mike Piazza and Tim Salmon in 1993 and Scott Rolen and Nomar Garciaparra in 1997. The Dodgers had five-time All-Star Adrian Gonzalez at first base.
Judge received all 30 first-place votes in the voting conducted by the Baseball Writers' Association of America.
Dodgers shortstop Corey Seager was the unanimous victor a year ago.
The award gives the Dodgers back-to-back Rookie of the Year Award Winners, and 18 total in franchise history, nine more than any other team in baseball.
Bellinger, meanwhile, earned his National League Rookie of the Year nod over Josh Bell of the Pittsburgh Pirates and Paul DeJong of the St. Louis Cardinals.
Pepsi was the official soft drink of Major League Baseball for the past 20 years, leading up to this season, when Coca-Cola took over.
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The Yankees outfielder and finalist for the Rookie of the Year will serve as the new spokesperson for Pepsi, the soda giant announced Monday. But they were 9-11 when they promoted Bellinger on April 25 - as an outfielder, following injuries to Andre Ethier and Joc Pederson. The Dodgers went 89-38 in the games Bellinger started, a.701 winning percentage.
The Dodgers advanced to the World Series, but Bellinger batted.143, with one home run and 17 strikeouts in 28 at-bats.
"Now that the season is over, I'm trying to reflect on how insane this season was", Bellinger said on MLB Network.
In the season's final month, Judge hit 15 home runs and knocked in 32 as the Yankees locked down a wild card. he led the league in FanGraphs WAR (8.2).