The players received their awards Monday before Game 5 of the World Series.
"I want to congratulate Jose and Matt on their fantastic seasons and express my gratitude to the Hall of Famers and fans who helped select this year's winners," Aaron said in a statement.
Bautista hit 43 home runs to lead the majors for the second year in a row. The slugger, who belted 54 homers last season, also batted a career-best .302 and knocked in 103 runs.
He led MLB with a .608 slugging percentage and 132 walks, and was second in the majors with a .447 on-base percentage. Bautista was also the first AL player since Babe Ruth in 1930 to record at least 40 homers, 130 walks and nine stolen bases in the same season.
Kemp, meanwhile, was third in the NL with a .324 batting average and hit a league-leading 39 homers with a league-best 126 RBI. He also topped the NL with 115 runs and 353 total bases.
He ranked second in the NL in hits (195), slugging percentage (.586), extra- base hits (76) and tied for second with 40 stolen bases.