In exchange, the Royals receive catcher Lucas May and right-hander Elisaul Pimentel.
Podsednik is having a solid year in his only season in Kansas City, batting .309 with 30 steals.
The Dodgers have been playing short-handed in the outfield, having placed Manny Ramirez on the disabled list July 21 with a strained calf.
Los Angeles entered Wednesday's play five games out of first in the NL West and 2 1/2 games out of the wild card.
Podsednik, who will be a free agent at the end of the season, is owed roughly $650,000 for the duration of 2010.