During the 2013 season, Berríos played for the Cedar Rapids Kernels of the Class A Midwest League where he was 7–7 with a 3.99 ERA in 19 starts. Berríos started 2014 with the Fort Myers Miracle of the Class A-Advanced Florida State League. He was selected to play in the All-Star Futures Game in July. After going 9–3 with a 1.96 ERA in 16 starts, he was promoted to the New Britain Rock Cats of the Class AA Eastern League on July 7. In eight starts for New Britain, he pitched to a 3–4 record and 3.54 ERA. He also played in one game for the Rochester Red Wings of the Class AAA International League at the end of the season.

Berríos has played for the Puerto Rican national team twice, in the 2013 World Baseball Classic and in the 2017 World Baseball Classic, winning in both tournaments the silver medal.

The Twins promoted Berríos to make his major league debut on April 27, 2016. In 18 innings pitched for Rochester prior to his promotion, he was 2–0 with a 1.06 ERA and 20 strikeouts. He was recalled and optioned multiple times during the season. In 14 starts for Minnesota, he was 3–7 with an 8.02 ERA, and in 17 starts for Rochester, he was 10–5 with a 2.51 ERA.

Berríos began 2017 with Rochester. After going 3–0 with a 1.13 ERA in six starts there, he was promoted to the Twins on May 13, where he spent the remainder of the season. In 26 games (25 starts) with Minnesota, he was 14–8 with a 3.89 ERA.

During the offseason, Berríos went to his hometown of Bayamón and delivered water, food, and other supplies to people in need as a consequence of Hurricane Maria which caused massive damage to Puerto Rico in September 2017.

Berríos began 2018 in Minnesota’s starting rotation and made his first start of the 2018 season on April 1, 2018. He pitched a complete game three-hit shutout (the first of his career) against the Baltimore Orioles, with 6 strikeouts, leading the Twins to a 7–0 win. Berrios tied his career high 11 strikeouts on April 12, 2018 in a 4–0 win over the Chicago White Sox. On April 18, 2018 Berríos finished with five strikeouts and no walks in seven scoreless innings for Minnesota in a game played in his native Puerto Rico before a sold-out crowd at the Hiram Bithorn Stadium. Berrios became only the second Puerto Rican pitcher to start a regular-season MLB game at Hiram Bithorn; the first being Javier Vazquez, who made four starts there in 2003 with the Montreal Expos. His second career complete game came on June 7th against the Chicago White Sox, he became the 9th Twins pitcher to pitch a complete game and strikeout at least 10 batters without allowing a walk.

On March 5, 2019, it was reported that Berrios would start opening day against the Cleveland Indians. He went 7.2 innings and had 10 strikeouts while not allowing a run. He received the win and the Minnesota Twins won 2–0.

On July 3, 2019, it was announced that Berríos would participate in the 2019 MLB All-Star Game.

With the 2020 Minnesota Twins, Berríos appeared in 12 games, compiling a 5-4 record with 4.00 ERA and 68 strikeouts in 63.0 innings pitched.