Los Angeles landed perhaps the biggest name available right at the trade deadline. The Rangers will receive three minor leaguers: second baseman Willie Calhoun, right-hander A.J. Alexy and shortstop Brendon Davis. They are the fourth-, 17th- and 27th-ranked prospects in the Dodgers' system, respectively, according to MLB.com.
Los Angeles did not want to part with top prospects such as right-hander Walker Buehler and outfielder Alex Verdugo.
"It's an honor to be wanted by the team," Darvish, who is from Japan, said through an interpreter.
Darvish is 6-9 with a 4.01 ERA this season, his worst in five years in the majors. A four-time All-Star, Darvish has seen his win total decrease in each of his seasons in the league -- from 16 in 2012 to seven last season. Tommy John surgery cost him the entire 2015 season.
Rangers manager Jeff Banister said he wished Darvish luck and challenged him to do something memorable.
"There were times where he was just dominating as we've seen previously with the fastball, the swing-and-miss slider, the sinker, the split, slow curve,'' Banister said. "He's going to wipe out hitters on days when his stuff is there. You're going to sit back and watch, and just marvel at what he does.''
Darvish, 30, is 0-5 with a 5.81 ERA over his past eight starts. He was tagged for a career-worst 10 runs in his last outing, and later revealed that he was tipping his pitches to the Marlins.
"I was mentally prepared for the announcement," Darvish said of the trade rumors, though only minutes before that he had tweeted a picture of himself wearing a Rangers cap while at his locker.
At Globe Life Park, where the struggling Rangers were set to host Seattle, Darvish said he had "nothing but appreciation" for his time in Texas.
Darvish can become a free agent after this season. Asked whether he would consider a return to the Rangers, he said he would have to wait and see.
Dodgers rookie first baseman Cody Bellinger tweeted a greeting to Darvish even before the deal was official.
Rangers president of baseball operations and general manager Jon Daniels said his team wanted to capitalize on the opportunity to add three talented young players. He said Darvish wasn't dealt because of the possibility that he wouldn't re-sign during the offseason.
"It really didn't play any role at all,'' Daniels said. "We know that if you don't sign your own free agent by Opening Day, usually he's going to test the market. ... I don't feel like the odds really changed a whole lot.''
The Dodgers, who are awaiting ace Clayton Kershaw's return from a back injury, are 74-31. They're seeking their first World Series title since 1988.
Calhoun, 22, hit .298 with 23 home runs and 67 RBIs in 99 games at Triple-A Oklahoma City.
Alexy, 19, was 2-6 with a 3.67 ERA in 19 starts at low-A Great Lakes. Davis, 20, hit a combined .241 with nine home runs and 43 RBIs at Great Lakes and high-A Rancho Cucamonga.
Information from The Associated Press was used in this report.