Galvis was born November 14, 1989, in Punto Fijo, Falcón, Venezuela, and at age 14, the Philadelphia Phillies began to scout him during his days playing youth baseball. He participated on Latin America’s team in the Little League World Series, but due to his slight stature (5 feet 10 inches (1.78 m) 154 pounds (70 kg)), struggled to captivate scouts’ attention. Galvis said, “They told me that I couldn’t play (pro) baseball. But I knew I had the ability.” In 2006, scouts Sal Agostinelli and Jesus Mendez signed him during the amateur player signing period. Galvis, 16 years old, was not a particularly heralded prospect, but did receive some attention from scouting experts before signing with the Phillies.

Galvis participated in the Florida Instructional League in 2006. The next season, he officially began affiliated baseball in 2007 with the Williamsport Crosscutters at age 17, as one of just five players not born in the United States. He made an impression with Phillies’ personnel due to outstanding defensive skills that drew comparisons to those of Baseball Hall of Famer Omar Vizquel, and also demonstrated solid instincts while baserunning, despite struggling to get on base. Concurrently, he hit .203 with nine stolen bases in 38 games. In 2008, with the Lakewood BlueClaws in the South Atlantic League, Galvis hit .238 with 14 stolen bases in 127 games. He had a particularly strong May, during which he hit .313 with 14 RBIs. He also earned placement on the league’s postseason all-star team. He began 2009 with the Clearwater Threshers in Class A-Advanced, and was the Phillies minor league player of the week after he hit .417 from April 20 to 26. The following May, he fractured his right ring finger, and spent more than two months on the disabled list. Thereafter, he spent seven games with the GCL Phillies before finishing the season at Double-A, where he hit just .197.

Galvis returned to Reading for his 2010 season after earning an invitation to the Phillies’ major league spring training. He led all shortstops in the Eastern League in fielding percentage, assists, putouts, and total chances. He was named an Eastern League all-star. After the season, he played for Navegantes del Magallanes in the Venezuelan Winter League. Entering 2011, he was “considered major-league-ready defensively but a major liability offensively.” But in 2011, at age 21, Galvis had the best season of his career to date. Always known as an excellent defender, but mediocre hitter, he was finally able to improve at the plate, thanks in part to a much more rigorous off-season conditioning regimen, and also due to hitting higher in the batting order, where he was thus challenged to make greater offensive contributions by utilizing a more aggressive approach. He also improved his arm strength to the point that at least defensively, coaches and front office personnel felt he was ready to be a major league shortstop. Starting the year in Double-A (AA) with the Reading Phillies, Galvis hit .273, with 35 RBIs, in 464 plate appearances across 104 games. In August, Galvis was promoted to the Triple-A (AAA) Lehigh Valley IronPigs, with whom he hit .321 with nine multi-hit games and 13 runs scored in his first 23 games. He hit in the leadoff spot with Lehigh Valley as well. Overall with Lehigh Valley, he hit .298, with eight RBIs in 126 plate appearances during 33 games. Between AA and AAA, he combined to hit .278 with eight home runs, 43 RBIs, 78 runs, and 23 stolen bases in 137 games. His excellent numbers were enough to earn the 2011 Paul Owens Award, which is given to the best position player and pitcher, respectively, in the Philadelphia Phillies minor league system. At the end of the 2011 season, Galvis was sent to the Venezuelan Winter League, and despite a brief ganglion cyst injury, played there until December 1.

Galvis was disappointed to learn that Phillies’ shortstop Jimmy Rollins had re-signed with the Phillies during offseason preceding 2012, as Galvis had hoped to replace him. He said that he allowed himself to pout for two hours, and then moved on. With Rollins re-signing with the Phillies, Galvis thought he was headed back to the minor leagues. He entered spring training as the “one of the most intriguing story lines” for the Phillies, and led the team in several statistical categories, but still presumed to open the season in AAA. However, on March 19, 2012, Phillies general manager Rubén Amaro, Jr. announced that Chase Utley would miss the beginning of the season due to a knee injury, and Galvis would be the opening day starter there.

Galvis struggled off the field after his injury in 2012, noting that he only emerged from the covers of his bed to answer the door for takeout food, mainly Chinese food, pizza, and cheesesteaks. Since then, he has started a daily therapeutic routine aimed at preventing future injuries, to which he is apparently susceptible after his first back injury. His hobbies include relaxing at the beach and playing basketball. Galvis married his wife, Anna, in 2013, and is the father of two girls named Anastasia and Nicole.

There was considerable debate as to whether Galvis should open the 2013 season working on his hitting in AAA, or on the bench of the major league Phillies. Manager Charlie Manuel preferred the latter, commenting that even in 300 major league at bats splitting time between second base, shortstop, and third base, Galvis could make a greater contribution than in a season in the minor leagues. Ultimately, he did make the opening day roster, but struggled through the first third of the season, and was optioned to AAA on June 27. Correspondingly, the Phillies acquired veteran infielder John McDonald. He performed better in AAA, including a 40-game streak during which he did not commit any errors, and a leadoff home run on the Fourth of July. He returned to the major league Phillies as a September callup, and on September 7, 2013, he compiled four hits including a game-winning home run against the Atlanta Braves. Overall, 19 at second base, 14 at third base, 10 in left field, and six at shortstop comprised his 49 total major league starts. At the major league level, he hit .234 with six home runs and 19 RBIs, and in AAA, he hit .245 with three home runs and 25 RBIs.

Galvis had a mixed year in the 2016 season both defensively and offensively. He led all National League shortstops in fielding percentage (.987) and was nominated for a Gold Glove Award, ultimately losing to Brandon Crawford of the San Francisco Giants. Offensively, Galvis collected 20 home runs and 67 RBIs with a .241 batting average in 158 games played. On the other hand, his .274 on base percentage was the lowest of all qualified major league batters.

Galvis played all 162 games in the 2017 season, including 155 games started at shortstop. On Opening Day, he hit a home run in the second inning against the Cincinnati Reds, one of 12 he would hit that season. Despite playing every game with the Phillies, Galvis slowly began to lose playing time at shortstop to top Phillies prospect J.P. Crawford following Crawford’s September callup. Galvis finished with a .255 batting average and .690 OPS. He also performed well defensively, again leading National League shortstops in fielding percentage and being nominated for a Gold Glove Award, and again losing to the Giants’ Brandon Crawford.

On December 15, 2017, Galvis was traded to the San Diego Padres for minor league pitcher Enyel De Los Santos. He opened the 2018 season as the Padres’ starting shortstop, and again played in all 162 games this season. This included 157 starts at shortshop and five starts at second base, in a season in which Galvis batted .248 with 13 home runs and a .680 OPS. He also recorded the highest shortstop fielding percentage for the third consecutive season. At the end of the season, Galvis became a free agent.

On January 29, 2019, Galvis signed a one-year, $4 million contract with the Toronto Blue Jays. The contract includes a club option for the 2020 season.

On August 12, 2019, Galvis was claimed off waivers by the Cincinnati Reds.