Jay batted .291 with two homers and 26 RBIs in 90 games with San Diego last season. He made his major league debut with St. Louis in 2010 and is a .287 hitter in 847 career games over seven seasons.
The Cubs have an opening in centre after Fowler turned down a $17.2 million qualifying offer two weeks ago. Fowler also rejected a qualifying offer from Chicago last November and then returned to the Cubs during spring training, but that same scenario seems even less likely this time around.
Jay could platoon in centre with righty-hitting Albert Almora Jr., or manager Joe Maddon could move Jason Heyward over from right for Chicago's first title defence since it won it all in 1908.
The Cubs announced the deal with Jay on Tuesday.