He has previously played in Major League Baseball (MLB) for the Houston Astros, Philadelphia Phillies, San Diego Padres, Chicago White Sox, and Pittsburgh Pirates.

A growth spurt prior to his senior year of high school caused him to draw interest from the soccer and gridiron football teams, but Velasquez opted to focus on baseball on the advice of a scout for the Chicago White Sox.

The Astros selected him in the second round of the 2010 MLB Draft, and Velasquez chose to pitch for them rather than honor his commitment to play college baseball as a shortstop for Cal State Fullerton.

He had a successful season with the Quad Cities River Bandits in 2013, but struggles during a three-game stretch with the Lancaster JetHawks inspired him to sharpen his curveball.

By 2020, Velasquez's inconsistent performance had placed his role on the Phillies roster in question, and he took advantage of the MLB's pause to diversify his pitch repertoire and improve his efficacy against batters.

A scout for the Chicago White Sox dissuaded Velasquez from pursuing other sports, warning him that an injury in football or soccer would compromise his baseball career.

[1] Velasquez pitched his first complete game on May 21, 2010, against the San Dimas High School Saints, the reigning California Interscholastic Federation (CIF) Southern Section division champions.

[1] At the time, he had already committed to play college baseball as a shortstop for Cal State Fullerton, but he chose to sign with the Astros after the team indicated that they would prefer him as a pitcher.

[7] Velasquez signed with the team on June 22, 2010, the day after his high school graduation, and was assigned to the Rookie Greeneville Astros of the Appalachian League.

[9] After spending the offseason building his strength and working on improving his strikeout-to-walk ratio, Velasquez began the 2013 season with the Single–A Quad Cities River Bandits.

He realized that, at higher levels of baseball, simply having a strong fastball was insufficient to strike out batters, and he spent the offseason working on a curveball to supplement his primary pitch.

After giving up four hits and three runs in one inning, Velasquez left his final scheduled start of the season with a strained latissimus dorsi muscle.

[22] He made his major league debut on June 10, pitching five shutout innings against the Chicago White Sox before the bullpen gave up three home runs, leading the Astros to a 4–1 loss.

[23] With the acquisition of Scott Kazmir in July, the Astros moved Velasquez to the bullpen, where the shorter innings requirement improved his velocity and focus on the mound.

[27] It was Matt Klentak’s first major trade as the Phillies' general manager; he used Giles as a bargaining chip to attempt a rebuild of a struggling team.

[33] Velasquez was named to the Phillies' 2017 opening day roster as the fourth starter in a five-man rotation with Jeremy Hellickson, Jerad Eickhoff, Clay Buchholz, and Aaron Nola.

[37] On August 22, the Phillies announced that Velasquez was suffering from restricted blood flow to the finger, and that he would be placed on the 60-day disabled list while he recovered from surgery.

[25] In 2018, Velasquez was part of an opening day rotation that was undergoing several changes: Jake Arrieta, despite being scheduled to pitch on April 8, was not officially named to the 25-man roster, while Eickhoff began the season on the injured list and Eflin was optioned to make room for Ben Lively.

[39] On June 30, a 97 mph (156 km/h) line drive off the bat of Adam Eaton hit Velasquez in his right arm, requiring the pitcher to pull off his glove and make a left-handed throw to first base.

[1][47] On August 3, when a game against the White Sox went into the 14th inning, the understaffed Phillies placed Velasquez in left field and allowed outfielder Roman Quinn to pitch.

Although the White Sox ultimately won in the 15th inning, Velasquez kept the game alive when his 94.7 mph (152.4 km/h) throw from left field to home plate successfully threw out José Abreu.

He undertook a series of pitching lessons with assistant coach David Lundquist over FaceTime, with particular focus on improving his efficacy against left-handed batters.

[49] When the season eventually began on July 24, both Velasquez and Pivetta were given opportunities to start, as Zach Eflin was returning from injury, while Zack Wheeler was on paternity leave following the birth of his first child.

[54] After Moore was placed on the COVID-19 list, Velasquez was called to make his first start of the season on April 20,[55] in which he gave up two runs in four innings of an eventual 5–4 walk-off loss to the Colorado Rockies.

[56] May proved to be the best streak of Velasquez's major-league career; he posted a 2.84 ERA in five starts before a numb index finger led to his last-minute scratch for a May 20 game against the Miami Marlins.

[57] The following month, Velasquez became involved in an ongoing MLB controversy regarding pitchers' use of foreign substances to increase spin rate and pitch control.

In the third inning of a June 7 game against the Washington Nationals, Velasquez lost control of a 90 mph (140 km/h) fastball, striking and accidentally fracturing the nose of opposing pitcher Austin Voth.

[58] Nationals manager Dave Martinez suggested that injuries of that sort would be more common if MLB banned the use of foreign substances that were supposed to enhance pitch grip, saying, "I understand them trying to clean some stuff up.

At the end of the season, Velasquez and manager Joe Girardi agreed that the pitcher would need to expand his repertoire and "learn to locate something away from righties and in on lefties".