He defected from Cuba in 2016 to establish residency in Haiti, where he first signed with the Los Angeles Dodgers as an international free agent.

Yordan Alvarez played two seasons in the Cuban National Series (CNS) for the Leñadores de Las Tunas.

[4] In August 2016, the Dodgers, in need of relief pitching, traded Alvarez to the Astros for Josh Fields,[6] before he played a single game in the minors.

[4] Dodgers President of Baseball Operations Andrew Friedman later acknowledged that trading Alvarez was "a mistake" and admitted, "I obviously wish I would have said yes to other names [the Astros] asked for before him."

[7] Alvarez made his professional debut in 2016 with the Dominican Summer League Astros, where he spent the rest of the year, batting .341 with a .974 OPS in 16 games.

[18] On June 9, 2019, the Astros selected Alvarez's contract and promoted him to make his major league debut that afternoon versus the Baltimore Orioles.

[20] Alvarez became the fourth player in Major League Baseball (MLB) history to hit four home runs in his first five career games when he homered off of Clayton Richard of the Toronto Blue Jays, joining Trevor Story, Yasiel Puig and Mike Jacobs.

[22] He won the American League (AL) Rookie of the Month Award for both June and July — the first Astro to do so — after garnering 48 hits, batting .336, 13 doubles, 13 homers and 39 RBI, .699 slugging, and 1.120 OPS.

He also led MLB with a 1.120 OPS since his debut, and was second in the AL with a .421 OBP, fourth in SLG, sixth in RBI, and seventh in average.

[23] On August 10, Alvarez hit a grand slam and homered twice more at Camden Yards for his first three-home run game in a 23–2 romp over the Orioles.

[26] The following day, he hit home run numbers 23 and 24 in 15–0 win versus the Oakland Athletics to break Carlos Correa's franchise record for rookies, set in 2015.

Alvarez also led AL rookies in on-base percentage (OBP, .412) and extra base hits (53), and was second in HR and RBI.

Likewise, the Houston chapter of the Baseball Writers' Association of America (BBWAA) voted Alvarez as the Astros' Rookie of the Year.

[39] In Game 5 of the ALCS, the Astros faced Boston Red Sox pitcher Chris Sale at Fenway Park in a 9–1 win.

Alvarez logged three hits and three RBIs versus the left-handed ace, all to the opposite field, including one home run that cleared the Green Monster.

[43] On June 2, 2022, Alvarez signed a six-year contract extension with the Astros worth $115 million; the deal bought out three remaining free-agent years that would keep him on the team until the 2028 season.

[47] Alvarez returned to play as DH versus Los Angeles after missing two games due to the collision with Peña, going 0-for-4 with a walk.

[49] On July 5, he hit his 25th home run and turned his first career double play, first catching a Nicky Lopez fly ball.

Alvarez then rifled the ball to Martín Maldonado at home plate on a 92.5 miles per hour (148.9 km/h) carom, who tagged out Hunter Dozier.

[53] Alvarez hit his 30th home run on July 29 versus the Seattle Mariners to establish a team record for reaching the mark in the fewest appearances, doing so in his 84th game of the season.

[58] On September 16, Alvarez led the Astros to a 5–0 victory over the Oakland A's with a 4-hit performance, including three home runs in consecutive at bats off starter Adrián Martínez.

[a][68] Offensively, Alvarez' 1.054 win probability added (WPA, 105.4f%) surpassed David Freese's 2011 World Series walk-off home run game for highest ever in an MLB postseason contest.

[76] Per an OptaSTATS tweet on July 31, "one of the most accurate predictors of the Houston Astros' success appears to be Yordan Alvarez' ability to get on base."

[84] Despite falling to the Rangers in 7 games, Alvarez continued to produce in the ALCS, batting .481 with two home runs, 9 RBIs, and posting a 1.309 OPS.

Alvarez was named the starting designated hitter for the American League All-Star team for the first time in his career and his third straight selection.

He joined teammate Jose Altuve, who hit for the cycle the season prior, as the most recent Astros to complete the feat, and 11th in club history.

It was the second time in club history with co-Players of the Week; on September 10, 2000, Richard Hidalgo and Julio Lugo shared the honors.

[90] On September 1, Alvarez reached 30 home runs for a fourth consecutive season, joining Bagwell (8 total, from 1996–2003) as the only Astros to have done so.

Among qualified American League batters, Alvarez ranked fourth in each of batting, on-base percentage, slugging, OPS, situational wins added (5.4), and championship WPA (2.1).

It was during a contest at Minute Maid Park versus the Minnesota Twins on August 23, 2022, that his family first saw him play professionally since leaving Cuba.