The deal is pending a physical, which could take place as soon as Tuesday. The person spoke on condition of anonymity because the team had not announced the agreement.
Okajima spent th e 2007-11 seasons with the Boston Red Sox, then signed a minor league deal with the New York Yankees and was released at the start of spring training when he failed a physical.
The 37-year-old was 1-0 with a 4.32 ERA in 8 1-3 innings over seven relief appearances for Boston in 2011 and 8-1 with a 2.29 ERA in 34 relief appearances with Triple-A Pawtucket. An All-Star as a rookie in 2007, he is 17-8 with a 3.11 ERA and six saves in five major league seasons.
Oakland manager Bob Melvin declined to discuss Okajima on Monday.
The San Francisco Chronicle first reported the pending contract.