Soler played for the Cuban national baseball team in the 2010 World Junior Baseball Championship, where he had a .304 batting average, .500 on-base percentage, and .522 slugging percentage. His nine walks were the second most in the tournament. Cuba won the bronze medal. Soler also played briefly with the Industriales in the Cuban National Series.
Soler defected from Cuba in 2011 to pursue his career in Major League Baseball (MLB). He established residency in Haiti. Soler was unblocked by the Office of Foreign Assets Control on June 2, 2012, making him a MLB free agent. As a free agent, many teams were involved in bidding on Soler's services.
Soler is 6 feet 4 inches (1.93 m) and weighs 215 pounds (98 kg). He was described as a power-hitting outfielder who would likely play right field. Jim Callis of Baseball America described Soler in 2011 as "a 19-year-old athlete with five-tool potential." According to Callis, Soler likely would have been a top-five pick in the 2010 draft had he been eligible. Kevin Goldstein of Baseball Prospectus did not rank Soler in his list of the top baseball prospects prior to the 2012 season, but said he would have ranked Soler as the 38th or 39th best prospect if he were eligible. Some teams preferred Soler to higher profile Cuban defector Yoenis Céspedes. Keith Law of ESPN.com indicated that Soler had the talent of a top-five draft choice in the 2012 Major League Baseball Draft, had he been eligible to be drafted. Writing for Fox News, Mauricio Rubio wrote that "Early in his career he was benched for not hustling, and in a separate incident he ran toward an opposing dugout with a bat." Writing for the Sporting News, Jeff Mans noted that: "The biggest issue with Soler aside from the hamstring injuries is his temper.... He started out on the wrong foot with the Cubs after failing to report to minor league camp shortly after signing his nine-year, $30 million deal, feeling that he should have been in Chicago immediately. The other scare for the Cubs brass was his relative inability to hit righthanded pitching."
According to Statcast, Soler's average launch speed was 91.39 miles per hour (147.08 km/h) in 2016.
On June 11, 2012, Soler reportedly agreed to a nine-year $30 million contract with the Chicago Cubs. The Cubs had reportedly agreed to a deal with Soler before he was declared a free agent, though Cubs general manager Jed Hoyer denied this.
On April 10, 2013, while playing on the Daytona Cubs of the Class A-Advanced Florida State League, immediately following a bench-clearing incident, Soler charged the opposing Clearwater Threshers' dugout while brandishing a baseball bat. He was ejected from the game, was fined, and received a five-game suspension.
Soler began the 2014 season with the Tennessee Smokies of the Class AA Southern League. On July 22, 2014, Soler was promoted to the Iowa Cubs of the Class AAA Pacific Coast League.
On August 25, 2014, Soler was called up to the Chicago Cubs for the first time. In his major league debut on August 27, facing Cincinnati Reds pitcher Mat Latos, Soler hit a home run in his first major league at-bat, becoming the 117th player in MLB history to do so. On September 1 Soler had two doubles in his home debut for the Cubs to become just the third major league player in the last 100 years to have at least one extra-base hit in each of his first five games in the majors. Two days later Soler became the second player in Cubs history with as many as 10 RBIs in his first seven games as a major leaguer. Soler was the starting right fielder for the Cubs 2015 season until an ankle injury sidelined him in early June. He returned to the starting lineup on July 5 after spending time in rehab. He finished the regular season with a .268 batting average, 15 home runs and 67 runs-batted-in.
In Soler's postseason debut, he walked as a pinch-hitter in the ninth inning in Game 1 of the Division Series and followed up with a double, two-run home run to straightaway center and two more walks in Game 2, and another home run, a single and two walks in Game 3. Record setting Soler started his postseason career by reaching base nine times in a row, in which he recorded five walks and hit two home runs, a double and a single. In Game 4 Soler ended a game-tying St. Louis Cardinals sixth inning rally with an outfield assist on a game-saving inning-ending put out of Tony Cruz at home plate. The Cubs won the game 6–4 and beat the rival St. Louis Cardinals in four games to advance to the National League Championship Series. Soler and the Cubs went on to win the 2016 World Series.
On December 7, 2016, the Cubs traded Soler to the Kansas City Royals for Wade Davis. After a string of injuries and inconsistency at the plate, Soler was demoted to AAA on June 2nd.