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 like 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 a translator.
The trade came after the Dodgers acquired left-handed relievers Tony Watson from the Pirates and Tony Cingrani from the Reds.
Darvish is 6-9 with a 4.01 ERA his season, his worst in five years in the majors. A four-time All-Star, Darvish has seen his win total decrease in each season in the league -- from 16 in 2012 to seven last season. Tommy John surgery cost him the entire 2015 season.
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.
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.
The Dodgers, who are awaiting ace Clayton Kershaw's return from a bad back, are 74-31. They're seeking their first World Series title since 1988.
Their rotation is now stacked with Kershaw, Darvish, Alex Wood, Rich Hill and Kenta Maeda or Brandon McCarthy.
Calhoun, 22, hit .298 with 23 home runs and 67 RBI 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.