[2][3] In November 2016, Robert defected from Cuba to pursue a Major League Baseball (MLB) career in the United States.

[10] In 2018, Robert made his first start at outfield in a spring training game and hit a two-out, go-ahead grand slam in the eighth inning, lifting the White Sox to a 14–12 victory over the Cincinnati Reds.

[17] On January 2, 2020, Robert agreed to a six-year, $50 million contract with the Chicago White Sox before appearing in a major league game.

[22] Robert hit his first postseason home run in Game 3 of the Wild Card Series against the Oakland Athletics off of Mike Fiers.

[24] Robert also finished second in balloting for the AL Rookie of the Year Award, losing to Kyle Lewis of the Seattle Mariners.

On July 14, 2022, in a game against the Minnesota Twins at Target Field, Robert hit his first career grand slam off of starting pitcher Sonny Gray.

[32] During a game against the Tampa Bay Rays on April 29, Robert was benched after not hustling to first base after hitting a ground ball to the third-base side of the mound.

[33] Robert won the American League Player of the Week Award on June 26 after he batted .444 with a 1.111 slugging percentage in the previous six games.

Robert announced he wouldn't be participating in the All-Star Game due to tightness in his right calf he suffered from the Home Run Derby.

On April 5, 2024, in a game against the Kansas City Royals, Robert suffered a Grade 2 flexor strain in his right hip while rounding first base in the ninth inning.

[39] The White Sox activated Robert from the IL on June 4 and made his return the same day against the Chicago Cubs at Wrigley Field.