The 24-year-old finished the regular season with 47 home runs, 34 doubles and a NL-leading 351 total bases.
Bellinger and Brewers star Yelich -- the 2018 NL MVP -- had been locked in a home run race all year.
However Yelich's season ended abruptly on September 10 when he suffered a broken kneecap in a freak incident, ruling him out of the final 18 games.
The award comes two years after Bellinger won Rookie of the Year honours. Bellinger is only the 18th former Rookie of the Year to go on to win the MVP award.
"This award, man, it just makes me so much hungrier to keep performing," Bellinger said. "The feeling that you have, why would you ever not want to receive this? So I have to keep working hard at what I do and hopefully keep getting better."
Despite his dazzling form in the regular season, Bellinger was largely ineffective in the postseason, when the Dodgers crashed out to eventual World Series winners Washington.
However, voting for the MVP award took place before the playoffs, so did not take into account postseason form.
The award, which is voted on by members of the Baseball Writers Association of America, sees two writers in each league city cast votes on a tabulated system.
First place picks earn 14 points, second place earns nine points, third place eight points. Bellinger was chosen as top pick by 19 voters, helping him to a total 362 points. Yelich earned 10 first place picks, with Rendon one.
Los Angeles Angels slugger Trout meanwhile is only the sixth player to win the American League MVP award three times, putting him alongside iconic figures such as Jimmie Foxx, Joe DiMaggio, Yogi Berra, Mickey Mantle and Alex Rodriguez.
Trout won 17 first place votes in the ballot, with Bregman netting 13.