The deal could be worth about $5.5 million if Duchscherer attains his incentives, the source said.
Duchscherer, a two-time All-Star, has a career record of 31-24 with the Athletics. He missed the entire 2009 season after undergoing elbow surgery in spring training and then seeking treatment for clinical depression.
The agreement won't be official until Duchscherer passes a physical exam, which isn't expected to take place until after Christmas.
Duchscherer will add a veteran presence to an Oakland rotation that includes young arms Trevor Cahill, Brett Anderson, Dallas Braden, Vin Mazzaro and Gio Gonzalez. In 2008, Duchscherer posted a 10-8 record with a 2.54 ERA in 22 starts with the Athletics.
Earlier this offseason, Duchscherer expressed an interest in signing a one-year contract so that he could re-establish himself and go back on the open market next winter. At least two other undisclosed teams made him offers before he decided to return to Oakland.
Duchscherer, 32, spent his first five professional seasons in Boston's organization. The Red Sox traded him to Texas for catcher Doug Mirabelli in 2001, and the Rangers later dealt him to Oakland for pitcher Luis Vizcaino in 2002.
Jerry Crasnick covers Major League Baseball for ESPN.com.