Moustakas, 29, played only 27 games in 2016 after sustaining an ACL tear in May. He bounced back this season to hit .272 with a career-high and franchise-record 38 home runs. He also had 85 RBIs.
"You're always hoping for a great year," Moustakas said. "But it's crazy to have a year like that."
Moustakas, the Royals' first-round Draft pick in 2007, is one of nine Royals free agents. With tight financial limitations, Kansas City is hoping the market will soften enough that it can afford to re-sign some of its free agents.
The Royals' previous single-season home run record was 36, set by Steve Balboni in 1985. Moustakas broke the record on Sept. 20 in Toronto.
"It's something I'll remember the rest of my life," Moustakas said.
Moustakas said he'll use the charity funds that come with winning the award to donate to the ACE 30 Fund in honor of late Royals pitcher Yordano Ventura. The ACE 30 Fund helps support youth baseball in Ventura's native Dominican Republic.
Jeffrey Flanagan has covered the Royals since 1991, and for MLB.com since 2015. Follow him on Twitter at @FlannyMLB. This story was not subject to the approval of Major League Baseball or its clubs.