The person spoke on condition of anonymity Thursday because the deal for the former star outfielder is subject to physical.
Jones can earn an additional $1.2 million in performance bonuses as part of the agreement: $150,000 each for 250 and 275 plate appearances, $200,000 apiece for 300 and 325, and $250,000 each for each of 350 and 375.
The 33-year-old Jones, brought in as a right-handed-hitting backup to Brett Gardner, Curtis Granderson and Nick Swisher, made an impact against New York in his rookie season, homering twice for Atlanta at Yankee Stadium in the 1996 World Series opener.
After hitting a career-best 51 homers for the Braves in 2005 and 41 the following year, his career nose-dived.
His home runs dropped to 26 during his final season with Atlanta and he hit three in 2007, his one injury-decimated season with the Los Angeles Dodgers. Jones rebounded to hit 17 homers for the Chicago White Sox in 2009 and had 19 last season for the White Sox to go along with a .230 average and 48 RBIs.