The person spoke on condition of anonymity Tuesday because the agreement had not yet been announced.
Flowers gets $2 million next season and $3 million in 2017. The agreement includes a $4 million team option for 2018 with a $300,000 buyout.
In addition, Flowers can make $1.5 million in performance bonuses each year based on starts at catcher, beginning at 55.
Flowers became a free agent last week when the Chicago White Sox failed to offer him a 2016 contract. The 29-year-old spent seven seasons with Chicago and hit .239 with nine homers and 39 RBIs in 112 games this year.