On July 29, 2021, the White Sox traded him to the Chicago Cubs for Ryan Tepera.[5] He finished the year with the High–A South Bend Cubs, compiling a 4.98 ERA with 24 strikeouts across 7 games (4 starts).[6] Horn split the 2022 campaign between South Bend and the Double–A Tennessee Smokies. In 33 appearances out of the bullpen, he registered a cumulative 2.79 ERA with 74 strikeouts and 4 saves over 51+2⁄3 innings of work.[7]
Horn split the 2023 season between the Double–A Tennessee Smokies and Triple–A Iowa Cubs. In 45 relief outings between the two affiliates, he accumulated a 7–3 record and 4.21 ERA with 78 strikeouts across 62 innings.[8] On November 14, 2023, the Cubs added Horn to their 40-man roster to protect him from the Rule 5 draft.[9]
Chicago White Sox (second stint)
On February 27, 2024, Horn was traded back to the White Sox in exchange for Matthew Thompson.[10] He was optioned to the Triple–A Charlotte Knights to begin the 2024 season.[11] After struggling to an 11.32 ERA in 9 games for Triple–A Charlotte, Horn was designated for assignment on April 26.[12]
Boston Red Sox
On April 30, 2024, Horn was traded to the Boston Red Sox in exchange for cash considerations. He was subsequently optioned to the Triple–A Worcester Red Sox.[13] Horn was promoted to the major leagues for the first time on June 28,[14] and made his debut the following day, against the San Diego Padres.[15]