Dodgers manager Joe Torre said Wednesday the club has signed Padilla, two days after the right-hander was released by Texas.
Torre said that Padilla will pitch Saturday at Triple-A Albuquerque before joining the Dodgers and will make his first scheduled start for his new team on Aug. 27 at Colorado.
Initially, the Dodgers had decided not to pursue Padilla. However, that was before Kuroda experienced post-concussion symptoms after being hit in the head by a line drive Saturday in Arizona.
Padilla, who was the Rangers' No. 2 starter when the season began, was 8-6 with a 4.92 ERA in 18 starts this season. Originally acquired in December 2005 in a trade with Philadelphia, Padilla was 43-34 with a 4.90 ERA over the last four seasons with the Rangers.
The Dodgers will owe Padilla less than $100,000 for the rest of the season -- a prorated portion of the minimum salary. The Rangers are responsible for the remainder of Padilla's $12 million salary this season.
Chad Billingsley returned to the Dodgers' rotation Tuesday after missing two starts with a hamstring injury. But he, Randy Wolf and Clayton Kershaw are the team's only remaining healthy starters from the group that started the season.
Jayson Stark is a senior baseball writer for ESPN.com. The Associated Press contributed to this report.