The 25-year-old Billingsley -- having recovered from a broken tibia, an injury sustained slipping on ice last winter -- went 9-4 with a 3.38 ERA over the first half of 2009 and was selected to the National League All-Star team.
But he skidded in the second half (3-7, 5.20), going winless over his final seven starts (0-5, 5.08) while receiving only six runs of support in those games. Billingsley, who twice encountered hamstring tightness, said late in the season that his struggles were the result of a mechanical flaw in his delivery.
He finished the regular season 12-11 with a 4.03 ERA, leading the team in victories and throwing 196 1/3 innings. But he was bumped from the rotation in the postseason, making only one appearance against Philadelphia in the National League Championship Series, allowing two runs in 3 1/3 innings.
Billingsley, who earned $475,000 last year, is expected to join Clayton Kershaw and Hiroki Kuroda in a rotation that does not have clear-cut candidates for the other two slots.
Billingsley's signing leaves the Dodgers with seven players eligible for salary arbitration -- Jonathan Broxton, Andre Ethier, Matt Kemp, Hong-Chih Kuo, James Loney, Russell Martin and George Sherrill.