Ms Jolie filed for divorce in 2016 and the pair have since been engaged in a custody battle largely shielded from public view.
A private judge hired to oversee the case, John Ouderkirk, ruled in Mr Pitt's favour.
The ruling would "significantly increase" his time with the children, a source told the Press Association.
Mr Pitt and Ms Jolie are parents to Pax, 17, Zahara, 16, Shiloh, 14 and 12-year-old twins Vivienne and Knox.
The oldest, 19-year-old Maddox, is not subject to the custody decision.
