Miller joins starters Jon Lester and John Lackey on his way out of Boston in an eventful day for general manager Ben Cherington, who has taken major steps to reshape his team with the Red Sox sitting in last place in the American League East with a 48-60 record.
"[Miller] probably pitched his way off the team because he pitched so well and because we are where we are and we have him for two more months," Cherington said. "Especially that type of pitcher is even more valuable for a winning team than he is for a team that's not winning as much so you have to listen to what you can turn that into. We had more calls on Andrew Miller than any other player on our team. Every contender in baseball pretty much called us on Andrew Miller because he fits for everyone -- he's a really good left-handed reliever, he's not making a lot of money. So there was a lot of teams involved.
"We felt like the single best player that we could get was Rodriguez in terms of potential upside and impact. There was a lot of good prospects we could have gotten for Miller. We like Rodriguez the best. As with the other guys, I don't think this rules anything out going forward but he's a Baltimore Oriole now and he's going to help them now try to get in the playoffs."
Miller, 29, is 3-5 with a 2.34 ERA and 69 strikeouts in 42 1/3 innings this season. He significantly improves a Baltimore bullpen that ranks 10th in the majors with a 3.36 ERA and is 18th overall with a batting average against of .242.
"Miller's emergence this year, being able to get out right-handers along with lefties, made him very attractive,'' Baltimore's executive vice president of baseball operations Dan Duquette said. "Not just to us. We ended up getting him, but there were a lot of other clubs that were in the market for left-handed relievers. His capabilities and his performance this year really distinguished himself from any other players in that position in the market.''
Duquette had been looking to upgrade the team's pitching depth in recent weeks. The Orioles sit in first place in the division at 60-46 and sport a 2½-game lead over the second-place Toronto Blue Jays.
"With the two really talented left-handed relievers at the end of the game, along with Darren O'Day, it gives us a very, very formidable backend of the bullpen," Duquette said.
The Red Sox began their sell-off last week when they traded veteran starter Jake Peavy to San Francisco for two pitching prospects.
Rodriguez, a 21-year-old Venezuela native, was rated Baltimore's No. 3 prospect by Baseball America entering this season. He's 3-7 with a 4.79 ERA in 16 starts with Double-A Bowie.
Information from ESPNBoston.com's The Associated Press was used in this report.