The Cubs will also receive Atlanta's international signing bonus slot No. 4, while the Braves acquire Chicago's No. 2, 3 and 4 slots.
La Stella hit .251 with one home run and 31 RBI as a rookie in 2014. His .328 on-base percentage and 36 walks led all National League rookies.
Vizcaino, 24, pitched five innings in 2014, giving up five earned runs and striking out four. His only other major league experience came in 2011, when he went 1-1 for the Braves with a 4.67 ERA and 17 strikeouts in 17.1 innings.
The Cubs finished 73-89 in 2014 and in last place in the NL Central. They recently fired manager Rick Renteria and replaced him with departed Rays manager Joe Maddon.
The Braves went 79-83 last season, finishing in third in the NL East.
- Molly Geary