The deal ends Heyward's tenure with his hometown team and lands a young pitcher to bolster Atlanta's rotation.
John Hart, the Braves' new general manager, signalled the start of a major overhaul after the team slumped to its first losing season since 2008. He dealt a player who was due to make $7.8 million next season and then become eligible for free agency.
The 25-year-old Heyward 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 as a rookie in 2013. He is not eligible for arbitration until after next season, so the deal represents a significant payroll savings for the Braves.
Walden made $1.49 million this past season and could have earned a raise in arbitration. He was 0-2 with a 2.88 ERA and three saves as a set-up reliever for closer Craig Kimbrel.
The Braves also acquired right-hander Tyrell Jenkins, who pitched for Class A Palm Beach this past season.
Miller joins a rotation that could look significantly different next season without free agents Ervin Santana and Aaron Harang, who combined for 26 wins. Kris Medlen and Brandon Beachy are both coming off their second major elbow operations, so a long-time strength of the team looked extremely thin heading into 2015.