A mediator in the couple's custody case hammered out a new agreement in November, stating that their adopted son, Roan, will spend one year with one parent and then the next year with the other, according to tabloid the Star.
The annual custody switch will continue for the next four years until the agreement is reviewed again.
Stone is shooting five films back-to-back this year and Bronstein felt the toddler would be better off staying at his home and attending school regularly, rather than traveling to various film sets.
Roan will be living in San Francisco, California, where his father is editor-in-chief of the San Francisco Chronicle newspaper.
Stone has another son, eight-month old Laird, whom she adopted after divorcing Bronstein.
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