Selected by the Blue Jays in the first round of the 2011 draft, Musgrove went straight from high school to the minor leagues. Houston acquired the big righthander one year later and he quickly became one of the top-rated pitching prospects in the organization.

Musgrove got a midseason call-up to the big leagues in 2016 and quickly made a big impression. In parts of two campaigns with Houston, the California native posted an 11-12 record with a 4.52 ERA in 49 games, 25 as a starter.

Musgrove was sent to Pittsburgh as part of the trade for Gerrit Cole and has since gone 17-21 with a 4.28 ERA in 51 games. Through 2019, he has compiled a 28-33 mark with 4.37 ERA in his four big league seasons.