The Baseball Writers Association of America announced the superstars as the winners of the awards on Thursday.
"This is unbelievable, and to be able to share it with all of these people who have been around a long time and had a positive influence on my life, it's really special," Yelich told MLB.com. "It's really hard to put into words what this means. You never dream of ever winning an award like this. It's been amazing."
Yelich, 26, led the National League with a .326 batting average, .598 slugging percentage, 1.000 OPS, 164 OPS+ and 343 total bases this season.
He also raked a career-high 36 home runs, plated 110 RBIs and had 22 stolen bases en route to his first All-Star selection. Yelich joined the Brewers in January as part of a five-player trade from the Miami Marlins.
Betts was the cornerstone of the Red Sox's World Series-winning squad. The 26-year-old outfielder led baseball with a .346 batting average, .640 slugging percentage and 129 runs scored. Betts also hit a career-high 32 home runs and had 30 stolen bases.
"It means a lot," Betts said. "It's definitely a special award and something that I'll cherish. But I think the most important thing is that we won a World Series and got to bring a trophy back to Boston."