Flowers was also signed to a one-year deal worth $4 million on Monday. He hit .229 (62-for-271) with 11 home runs, 34 RBI and a .733 OPS in 85 games for the Braves last season.
The Braves announced that the team has declined Teheran's team option for 2020.
Atlanta also has tendered the third baseman a qualifying offer. Donaldson hit .259 (142-for-549) with 37 home runs, 94 RBI and a .900 OPS in 155 games. He has 10 days to accept or reject the offer.