Galvis, who turns 30 on Nov. 14, was claimed by the Reds off waivers from Toronto on Aug. 12 and hit .234 with five homers and 16 RBIs in 32 games. Overall, he batted .267 last season and set career bests with 23 homers and 70 RBIs.
Cincinnati announced its decision Friday.
Mostly a shortstop with Toronto, Galvis played more at second with the Reds. Jose Iglesias, Cincinnati's regular shortstop this year, became a free agent Thursday.
Galvis' contract, agreed to with the Blue Jays in January, included a $4 million salary for 2019. If the option had been declined, he would have received a $1 million buyout.
He has a .248 career average in eight seasons with Philadelphia (2012-17), San Diego (2018), Toronto and Cincinnati.