The Arizona Diamondbacks selected Swanson with the first overall selection of the 2015 Major League Baseball Draft. Swanson signed with the Diamondbacks, receiving a $6.5 million signing bonus. While batting in a simulated game against Yoan López in July 2015, Swanson was hit in the face with a pitch. The injury delayed his professional debut, which took place on August 12, 2015, with the Hillsboro Hops of the Class A-Short Season Northwest League. Swanson played in 22 games in his first professional season and finished with a .289 batting average, one home run, fourteen walks, and eleven RBIs.
On December 9, 2015, the Diamondbacks traded Swanson, Ender Inciarte, and Aaron Blair to the Atlanta Braves for Shelby Miller and Gabe Speier. The Braves invited Swanson to spring training, and he was sent to the Carolina Mudcats of the Class A-Advanced Carolina League at the end of spring training. Swanson was promoted to the Mississippi Braves of the Class AA Southern League on April 30, 2016, after hitting .333/.441/.526 in 21 appearances at Carolina. On June 28, he was named to appear in the All-Star Futures Game, soon after having played the Southern League All-Star Game. On August 16, the Braves announced that Swanson would be promoted to the major leagues the next day. Upon his callup, Swanson was assigned jersey #2. On August 17, he went 2-4 in his MLB debut, including his first career hit off of Minnesota Twins pitcher Kyle Gibson. Swanson hit an inside-the-park home run against the Washington Nationals on September 6, his team's first such home run since 2001. With the hit, Swanson followed Paul Runge as only the second Braves player to ever make an inside-the-park home run with his first career big league home run. Swanson finished the year in the majors, recording a .302 batting average, .361 on-base percentage and a .803 on-base plus slugging percentage.