Musgrove has appeared in 49 games the last two seasons, going 11-12 with a 4.52 ERA and 0.7 WAR combined.
Houston is sending pitcher Joe Musgrove and third baseman Colin Moran as the principle members of the deal.
Martin, 22, was an eighth-round pick in 2013. In 338 plate appearances, he hit 18 homers with 31 walks and 55 strikeouts. He improved both his strikeout and walk rates a year ago, and the move to Minute Maid Park is an upgrade for Cole, both in terms of run prevention and strikeouts.
The Astros reportedly targeted Cole at the trade deadline last summer. If everything breaks right, the Astros are getting a gem here. He made $3.75 million in 2017 and avoided salary arbitration on Friday with a $6.75 million deal for 2018.
Cole should immediately slot into the Astros rotation alongside Justin Verlander, Dallas Keuchel, Lance McCullers Jr. and World Series hero Charlie Morton. The Astros likely were eager to get the deal done before those numbers were set.
Uriah Hall vs Vitor Belfort Scratched from UFC St. Louis
Louis card Sunday night that's highlighted by the main event of Jeremy Stephens taking on Doohoo Choi in a featherweight bout. In more than two decades of professional action, Belfort competed in across the globe in most of the major MMA organizations.
Cole, 27, can be a free agent after the 2019 season.
Cole has been the Pirates ace for the past several seasons.
Despite making a career-high 33 starts in 2017, Cole posted his worst ERA (4.26), worst home run rate (1.4 per nine innings) and second-most hits allowed per nine innings (8.8). With the Astros, Cole has a potent lineup with Jose Altuve and Carlos Correa leading the way and he can safely slot into the No. 3 spot in the rotation.
Even with those lackluster stats last season, Cole is the kind of pitcher the Astros can afford to take a chance on.