Lopez was 9-18 with a 5.90 ERA last season in 29 starts and seven relief appearances. His 18 losses were the most in the majors and matched the second-highest in club history.
Colorado general manager Dan O'Dowd said the Rockies liked the fact that Lopez pitched in the American League East and that he has shown the ability to log innings. Lopez threw 189 innings in 2006 and 209 1/3 the previous year.
"He gives up some hits, but he does pitch a lot of innings, and he has pitched in the toughest division in baseball," O'Dowd said. "We think he has a good chance to be a good pitcher here."
The fact Lopez has worked with catcher Javy Lopez in the past wasn't a consideration, O'Dowd said. Javy Lopez was signed to a one-year deal with Colorado on Tuesday. Javy Lopez finished the final season of a $22.5 million, three-year contract he signed as a free agent with the Orioles in December 2003.
Rodrigo Lopez made three Opening Day starts for Baltimore.
"We ended up getting two midlevel prospects for him that were not on the roster," Orioles vice president Jim Duquette said of the deal. "We like their arms. Like all minor-leaguers, they have some things to work on."
In five seasons with the Orioles, Lopez was 60-58 with a 4.72 ERA. He made $3.75 million last year and is eligible for salary arbitration, as are right-handers Jeremy Affeldt and Josh Fogg, second baseman Luis Gonzalez and outfielders Matt Holliday and Cory Sullivan.
Miller was 0-3 with 12 saves and a 3.86 ERA in 45 relief appearances last year for Tulsa, the Rockies' Double-A affiliate. Colorado picked him in the eighth round in the 2004 amateur draft.
Burch was 3-4 with a 4.95 ERA in 45 relief appearances in Tulsa last year. Burch was drafted by the St. Louis Cardinals in the 21st round in 2003 and was acquired by the Rockies as part of a trade that sent right fielder Larry Walker to St. Louis in 2004.
Baltimore also agreed to a $775,000, one-year contract with right-hander Todd Williams, who became a free agent last month when the Orioles failed to offer a 2007 contract.
Williams was 2-4 with one save and a 4.74 ERA in a team-high 62 relief appearances last year and made $775,000. In addition to his salary this year, he could earn $50,000 each for 65, 70 and 75 games and $25,000 each for 10, 15 and 20 games finished.
He is 9-9 with two saves and a 3.72 ERA in 163 games with the Orioles during the past 2½ seasons.