The trade is the first major move for the Braves under new general manager John Hart.
Heyward, 25, hit .271 with 11 homers and 58 RBI in 149 games last season with the Braves. A five-year veteran, Heyward is a two-time Gold Glove winner (2012, 2014) and owner of a .262 career batting mark with 84 home runs and 292 RBI to go along with 63 stolen bases.
Miller went 10-9 with a 3.74 ERA in 32 games (31 starts) last season. In 183 innings he struck out 127, walked 73 and allowed 160 hits.
In three big-league seasons, all with the Cardinals, Miller has a career 26-18 mark with a 3.33 ERA over 69 games (63 starts).
Atlanta was in the market for young starting pitching and had a surplus of position-player talent.
Walden, 27, struck out 62 batters in 50.0 innings pitched, posting an 0-2 record with a 2.88 ERA and three saves over 58 outings. The hard-throwing right-hander, who in 2011 led the Angels in saves with 32, is also a five-year veteran.
Jenkins is a minor-league pitcher who has a career mark of 18-15 with a 4.23 ERA in 58 starts between rookie league and Single-A.