The person spoke to the AP on condition of anonymity because the signing has not been announced. Foxsports.com first reported the deal.
The 32-year-old Fujikawa pitched for two-time World Baseball Classic champion Japan and played in the 2008 Beijing Olympics. He had 220 saves in 12 seasons with Hanshin and became an unrestricted free agent last month.
Fujikawa gets a $1 million signing bonus, and $4 million salaries in 2013 and 2014. The deal includes a vesting option for a third year at $5.5 million or $6 million based on games played.
If the option doesn't become automatic, the Cubs could then pay him $5.5 million or buy him out for $500,000. Fujikawa could also earn up to $2 million in performance bonuses per year.
The Cubs went 61-101 last season.