Volquez, who hasn't pitched in relief in six years, also likely will make some starts in the final month to give the Dodgers' rotation extra rest.
Dodgers starters have the best ERA in the majors, but with Stephen Fife recovering from a shoulder injury and Chris Capuano struggling, the team wanted to add some depth before the Aug. 31 deadline for players to be eligible for postseason play.
"We like his stuff and we like what we think he's capable of doing," Dodgers manager Don Mattingly said.
Volquez, 30, was an All-Star with the Cincinnati Reds in 2008, when he went 17-6 with a 3.21 ERA. However, he had given up more earned runs than any other pitcher in the majors this season before being released Tuesday by the San Diego Padres, with whom he was 9-10 with a 6.01 ERA.
The Dodgers optioned reliever Chris Withrow to Triple-A Albuquerque, but Withrow likely will return Sunday, when rosters expand.
Volquez is making $5.725 million this year, but the signing will not affect the Dodgers' payroll because they are responsible for only the prorated share of the major league minimum. The Padres will be on the hook for the rest.