The deal was announced Tuesday night and was the first trade at the winter meetings.
Lopez was 6-3 with 10 saves and a 2.17 ERA in 64 games for the Astros last season. Known for his sharp control, he struck out 54 and walked just eight in 66 1/3 innings. The 29-year-old righty has done well at inducing groundballs and spent the past four seasons with Houston.
The 24-year-old White split last season with the Rockies and Triple-A Colorado Springs. He was 2-9 with a 5.51 ERA in 23 games for the Rockies, including 20 starts. He was the 15th overall pick in the 2009 draft, taken by Cleveland.
The 23-year-old Gillingham was 6-8 with a 3.66 ERA at Class-A Asheville in his first full pro season.