The deal was announced Monday and ends Heyward's tenure with his hometown team.
The 25-year-old outfielder never lived up to expectations after a brilliant rookie season, when he homered in his first at-bat and was voted to the All-Star Game. This past season, he hit .271 with 11 homers, 58 RBIs and 20 stolen bases. He also won his second Golden Glove.
Miller went 10-9 with a 3.74 for the Cardinals, after going 15-9 with a 3.06 ERA in 2013.
Walden was 0-2 with a 2.88 ERA and three saves.
The Braves also acquired pitcher Tyrell Jenkins, who played for Class A Palm Beach last season.
