Meadows was considered as one of the top prospects eligible for the 2013 Major League Baseball draft. He was ultimately selected in the first round, with the ninth overall selection, by the Pittsburgh Pirates. Meadows was committed to attend Clemson University to play college baseball for the Clemson Tigers, but chose to forgo that commitment by signing with the Pirates, receiving a $3,029,600 signing bonus three weeks after the draft. After signing with the Pirates, Meadows played for the Gulf Coast Pirates of the Rookie-levelGulf Coast League and the Jamestown Jammers of the Class A-Short SeasonNew York–Penn League in 2013, compiling a combined.316 batting average with seven home runs and 22 RBIs in 48 games between both teams. He played for the West Virginia Power of the Class ASouth Atlantic League in 2014, but missed a significant portion of the season due to a hamstring injury, playing only 38 games, batting.322/.388/.486 with three home runs and 15 RBIs. He played for the Bradenton Marauders of the Class A-AdvancedFlorida State League in 2015, and was named an FSL All-Star. He spent the final week of the season with the Altoona Curve of the Class AAEastern League. In 121 games for Bradenton he slashed.307/.357/.407 with seven home runs and 54 RBIs, and in six games for Altoona he batted 360. After the regular season, he played for the Glendale Desert Dogs of the Arizona Fall League. Meadows suffered a broken orbital bone in his right eye during spring training in 2016. He returned to Altoona and earned a promotion to the Indianapolis Indians of the Class AAAInternational League in June. In 45 games for Altoona he batted.311 with six home runs and 23 RBIs in 45 games, and in 37 games for Indianapolis, he compiled a.214 batting average with six home runs and 34 RBIs. The Pirates invited Meadows to spring training in 2017. Meadows returned to Indianapolis for the 2017 season, where he posted a.250 batting average with four home runs and 36 RBIs in 72 games. He missed nearly two months of the season due to hamstring and oblique strains. The Pirates added him to their 40-man roster after the 2017 season. MLB.com ranked Meadows as Pittsburgh's second best prospect going into the 2018 season. He began the season with Indianapolis and was promoted to the major leagues to make his debut on May 18. He recorded his first major league hit off of Tyson Ross, as well as his first stolen base, that same night. On May 20, 2018, he hit his first major league home run off of Jordan Lyles. Meadows was named the National League Rookie of the Month for the month of May after batting.409 with four home runs, seven RBIs, three doubles, and three stolen bases in 13 games during the month.
On July 31, 2018, Meadows was traded to the Tampa Bay Rays, along with Tyler Glasnow and a player to be named later, later revealed to be Shane Baz, for Chris Archer and was optioned to Triple-A Durham. Meadows was promoted to the Tampa Bay Rays on September 19. In ten games with the Rays, hit.250/.308/.417 with a home run and four runs batted in. Meadows ended the season slashing.287/.325/.461 with six home runs and 17 runs batted in over 59 games. The next year he made his first All-star game. Meadows ended the season with career highs offensively. He led the team in average, home runs, runs and 89 runs batted in in 138 games. On July 16, 2020, it was announced that Meadows had tested positive for COVID-19.