After missing the 2016 season while recovering from Tommy John surgery, Holland was 3-2 with a 3.61 ERA and 41 saves. The 32-year-old right-hander tied with Kenley Jansen of the Los Angeles Dodgers for the second-most in the major leagues, six behind Tampa Bay's Alex Colome.
Moustakas hit .272 with a career-high 38 homers and 85 RBIs in his return from a torn anterior cruciate ligament in his right knee. The season-ending surgery happened when he collided with teammate Alex Gordon chasing a foul popup on May 22, 2016.
Holland and Moustakas became free agents after the World Series.
Major League Baseball announced the winners Friday. The awards, which began in 2005, are voted on by the 30 team beat writers from MLB.com.
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