The Padres received minor league pitchers Robbie Erlin and Joe Wieland.
Adams, who turned 33 on Friday, is 3-1 with a 1.13 ERA in 48 relief appearances as a late-inning setup man for the Padres. He has 49 strikeouts and nine walks and opponents are hitting just .155 against him.
Adams was a bit taken aback by the trade.
"I'm from Texas and it's quite a bit of a shock," he said. "The past couple of days, I didn't really think I'd be going anywhere. But this is [how] baseball works. Things happen and things happen fast. I'm excited about it."
Rangers general manager Jon Daniels said the club was open to a rental, but was it was not preferred. Heath Bell is an unrestricted free agent after the season. So Adams, who is under club control through 2012, was someone the club targeted. Koji Uehara, who was acquired on Saturday, is 12 appearances shy of a vesting option for 2012, meaning the Rangers' bullpen additions are more than just half-season rentals.
"(It) didn't seem like either side was going to get ultimately what they wanted unless they both compromised. We did that," Daniels said. "I think it's a good baseball trade on both sides, kind of a traditional baseball trade. We get a piece to help us win now and they get two young starting pitchers that I fully expect are going to have successful careers in the big leagues."
Combined, Uehara and Adams have pitched 95 innings and allowed 51 hits with 111 strikeouts and 17 walks. That's an upgrade to a bullpen that was 11th in the AL with a 4.42 ERA. Adams and Uehara have a combined 1.42 ERA.
Daniels said that Adams has the stuff to close games, but that he's a setup man with Neftali Feliz as the closer.
"I have no idea what the situation is over there. My biggest concern right now is going over there and putting up some zeroes," Adams said. "Whatever inning they want me to pitch, it's going to be refreshing. It's a totally different atmosphere there. They are all about winning. They were asking a lot to get me. If they put those prospects out there, they're serious."
The Rangers dealt two solid pitching prospects to get Adams. Erlin, a lefty, is 8-4 with a 3.34 ERA over his last 20 games (19 starts) with Class A Myrtle Beach and Double-A Frisco this season. He was taken by the Rangers in the third round of the 2009 June draft.
"We discussed trading (Bell and Adams). In the end, we had targeted the players we really wanted to acquire," Padres GM Jed Hoyer said. "The two Texas pitchers, they were guys that we had scouted heavily this year. It was pretty obvious for a long time that Texas was going to be a fit for us. ... Mike was the piece that they wanted."
Wieland is 10-3 with a 1.80 ERA in 21 games (20 starts) for Myrtle Beach and Frisco this season after getting promoted to Frisco in late June. He threw a no-hitter on Friday against San Antonio, allowing just one walk.
Wieland and Erlin are in the unusual spot of simply switching dugouts Sunday night in the Texas League. The Rangers' Double-A affiliate, Frisco, is playing in San Antonio against the Padres' affiliate.
Wieland said Scott Servais, Rangers' director of player development, called him to let him know what was going on.
"He said, 'You probably understand what goes on here at the trade deadline and we've traded you to San Diego with Erlin for Mike Adams,'" Wieland said. "My head is still kind of spinning. But for me looking at it, it's a win-win. If I was staying in this organization, that would be great. But I get to go into San Diego's system and it's a new start and it's a little closer to home."
Wieland is from Reno, Nevada. He said he's scheduled to pitch Thursday and Erlin is expected to go Tuesday for their new team.
He said he was told the no-hitter had little to do with the trade.
"They said they had been following me for my last five starts," Wieland said. "They said they wished I'd thrown it for them. But wasn't like the no-hitter put it over the edge."
Adams becomes one of the Rangers' tallest pitchers at 6-foot-5. He has held right-handers to a .107 average in 2011. His 1.13 ERA is the third-lowest among major league relievers. His .197 opponent on-base figure is third-lowest in the majors behind San Francisco's Sergio Romo and Uehara (.191).
Richard Durrett covers the Rangers for ESPNDallas.com. Information from The Associated Press was used in this report.