The people spoke on condition of anonymity Monday because there had yet to be a formal announcement. The AL West champion A's called a news conference for Tuesday afternoon described as a "major announcement."
Nakajima agreed to a $6.5 million, two-year contract. The deal also includes a $5.5 million option for a third season, one of the people said.
Nakajima, a seven-time Pacific League All-Star, has a .302 batting average with 149 home runs, 664 RBIs and 134 stolen bases over 11 seasons with Seibu.
He would fill a big void for Oakland, which traded away shortstop and second baseman Cliff Pennington to Arizona in an Oct. 21 trade that brought outfielder Chris Young to the A's.
The club also appears to have lost out on shortstop Stephen Drew, who was acquired in an August trade with Arizona. He batted .250 with five homers and 16 RBIs in 39 regular-season games with Oakland.
General manager Billy Beane's big priority has been to find a shortstop.