Valdez signed with the Houston Astros as an international free agent on March 19, 2015, for a $10,000 bonus. At age 21, he was five years older than most amateur free agent signings from his country. Two Astros scouts spotted him after a long day of viewing programs led by independent trainers. Watching him throw only six pitches—in the beams of car headlights as darkness fell—they offered him a tryout at their Dominican academy near Guayacanes. Valdez had had verbal agreements with seven teams prior to signing with the Astros, but each offer was withdrawn after the results of his physical revealed that he might require ulnar collateral ligament reconstruction, also known as "Tommy John surgery." Indeed, as a teenager, team after team declined to sign him for medical reasons that he "did not understand at all."

Valdez made his professional debut in 2015 with the DSL Astros, going 4–1 with a 3.68 ERA over 36+2⁄3 innings. He split the 2016 season between the Greeneville Astros, Tri City ValleyCats, Quad Cities River Bandits, and Lancaster JetHawks, combining to go 4–5 with a 3.19 ERA over 73+1⁄3 innings. He split the 2017 season between the Buies Creek Astros and the Corpus Christi Hooks, going a combined 7–8 with a 4.16 ERA over 110+1⁄3 innings. Following the 2017 season, he played for the Mesa Solar Sox of the Arizona Fall League.

He split the 2018 minor league season between Corpus Christi and the Fresno Grizzlies, going a combined 6–5 with a 4.11 ERA over 103 innings.
The Astros promoted Valdez to the major leagues for the first time on August 21, 2018. He made his debut that day, pitching 4+1⁄3 innings and earning the win. With Houston in 2018, he went 4–1 with a 2.19 ERA over 37 innings. Valdez split the 2019 season between the Round Rock Express and Houston. With Round Rock, he went 5–2 with a 3.25 ERA over 44+1⁄3 innings. With Houston, he went 4–7 with a 5.86 ERA over 70+2⁄3 innings.

It was after the season that he was urged by Caridad Cabrera, the team director of Latin American operations to see team sports psychologist Dr. Andy Nuñez at their Dominican academy. The two soon found a strong bond with each other, with Nuñez advising him on how he should harness his emotions better with controlled breathing in tense situations. He was cited as a key presence in Valdez's improvement as a pitcher, and the two still contacted each other prior to every Valdez start.

In 2020, Valdez was 5–3 with a 3.57 ERA in 11 games (10 starts), in which he threw 70+2⁄3 innings and struck out 76 batters (8th in the AL), and had the second-best home runs per nine innings allowed (HR/9 IP) ratio in the AL (0.637). He led the club in innings pitched, tied for the team lead in games won, and was named Astros Pitcher of the Year by the Houston chapter of the Baseball Writers' Association of America (BBWAA).

On September 29, 2020, in Game 1 of the American League Wild Card Series, Valdez became the first relief pitcher to throw five scoreless innings in the playoffs since Madison Bumgarner did so in Game 7 in the 2014 World Series. Valdez went 3–1 in the postseason, which saw the Astros reach the American League Championship Series (ALCS) after winning the first two rounds of the COVID-affected 2020 season. He was the winning pitcher in Game 6 of the L…

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Valdez is married with three children. Valdez is naturally right-handed and performs everyday tasks with his right hand; he taught himself to throw left-handed as a child knowing the value of such pitchers in baseball.

During Game 2 of the 2022 World Series at Minute Maid Park, Valdez' father, José Antonio Valdéz Ramírez, witnessed his son pitch for the first time in the major leagues. Valdez had not traveled previously to see him play due to a fear of flying.

Valdez is a Christian. He donated $100,000 to help build a church in his hometown.

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