Greinke, 35, is 10-4 with a 2.90 ERA in 22 starts this season. He allowed two runs in five innings against the Yankees on Wednesday afternoon.
The Diamondbacks acquired first baseman/outfielder Seth Beer, pitchers J.B. Bukauskas and Corbin Martin, and infielder Josh Rojas, according to ESPN and MLB.com. Beer, Bukauskas and Martin are considered the Diamondbacks' third, fourth and fifth-best prospects, according to MLB Pipeline.
Greinke is 197-122 since debuting in 2004. He is a six-time All-Star and won the American League Cy Young Award in 2009.
Geinke is under contract through the 2021 season.
Houston is 69-39 this season. The first-place Astros have an eight-game lead over the Oakland Athletics in the AL West Division.
Arizona entered Wednesday with a 54-54 record. The Diamondbacks are three games out of first place in the NL Wild Card race.