Fox Sports' Ken Rosenthal reports that the contract is worth $1.5 million.
Billingsley underwent Tommy John surgery in April 2013 and has not pitched in the majors since. While with the Los Angeles Dodgers last season, the 30-year-old made two rehab starts in the minors before undergoing elbow surgery.
In his last full season in 2012, Billingsley went 10-9 with a 3.55 ERA and 128 strikeouts in 149.2 innings.
Billingsley was drafted by the Dodgers in the first round of the 2003 MLB draft and had spent his entire career in Los Angeles.
- Molly Geary