MLB World Series champions the Astros dealt pitchers Joe Musgrove and Michael Feliz and third baseman Colin Moran to the Pirates in return for the 2015 All-Star.
Prospect Jason Martin is also heading to Pittsburgh.
Cole is coming off a career-worst ERA at 4.26 in 203 innings pitched, but he remains one of the hardest throwers in the game.
The 27-year-old was the number one overall pick in 2011 by Pittsburgh and is twice a first-round pick as he was taken 28th overall by the New York Yankees in 2008.
Houston will now feature a rotation with two Cy Young winners in Justin Verlander and Dallas Keuchel and a former top pick in Cole. Lance McCullers Jr. and Charlie Morton will likely round it out.
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