Feliz, 24, went 4-2 with a 5.63 ERA in 46 relief appearances with the Astros last season, drawing his career numbers to 12-3 with a 5.13 ERA in parts of three seasons in Houston.
Musgrove started 15 games for the Astros last season and had a 4.77 ERA. He finished this past season ranking tied for first in starts (33), third in innings pitched (203) and 10th in strikeouts.
Houston sent right-handers Joe Musgrove and Michael Feliz, third baseman Colin Moran and outfielder Jason Martin to Pittsburgh in the deal. With Dallas Keuchel hitting free agency after the 2018 season, Astros owner Jim Crane made no secrets that the team would seek out starting pitchers this winter.
The Astros reportedly targeted Cole at the trade deadline last summer.
Now, there's another intriguing arm in Cole added to the rotation.
Cole had signed a one-year extension with Pittsburgh on Friday for $6.75 million.
Moran, 25, has appeared in 16 games at the Major League Baseball level over the last two seasons.
Cole, 27, is in his second year of arbitration eligibility.
Martin, 21, was an eighth-round draft pick by the Astros in 2013. He was blocked at the hot corner in Houston by young slugger Alex Bregman but could pilfer at-bats from David Freese in Pittsburgh. "We just happen to have someone in front of him". Additionally, he averaged 8.69 strikeouts per nine innings with a 3.1 fWAR - the second-best mark of his career. Despite that, he had a 5.63 ERA in part because of subpar control. The 22-year-old batted.278 with 18 home runs and 16 stolen bases last season split between Class A Buies Creek and Double-A Corpus Christi.