The deal is pending a physical, a source told ESPN The Magazine's Buster Olney.
Padilla, who spent the past season and a half with the Dodgers before becoming a free agent this fall, presumably will pitch primarily out of the bullpen for the Dodgers, who already have five established starters, but he also would be a swing man who could step into the rotation if another starter is injured.
However, multiple sources also have said Padilla could be a candidate to fill the closer's role if Jonathan Broxton continues to struggle.
Padilla went 6-5 with a 4.07 ERA in 16 starts for the Dodgers last season, but he also missed significant time with two different injuries.
Padilla's contract also includes performance bonuses that could increase the value.
Tony Jackson covers the Dodgers for ESPNLosAngeles.com.