The ruling also authorised a monthly allowance for the 79-year-old from the singer's estate, the amount of which has not been disclosed but which is believed to be worth around £300 million in total.
Her three grandchildren – Prince Michael, 12, Paris, 11 and seven-year-old Blanket – were also granted a monthly allowance.
The decision followed an agreement last week between Katherine and the singer's ex-wife Debbie Rowe, who is the biological mother of the two eldest children.
Under the new agreement, Debbie – who was not in court - will have visitation rights to Prince Michael and Paris, and will continue to get spousal support payments following an arrangement with Michael in 2006.
In a bizarre twist, the hearing included a last minute move from Michael's dermatologist, Arnold Klein, who requested a role in the children's upbringing.
The doctor is rumoured to be the biological father of Prince Michael and Paris. When asked by the judge what his legal relationship was, Mr Klein's lawyer replied: "Legally he is not a presumed parent."
It was ruled he had no legal standing to object to the custody arrangement, but he could raise later objections if necessary.
Meanwhile, as Katherine looks forward to raising the children, she has spoken up to address claims that she and Michael's father Joe, 80, are estranged and that he is banned from the family home in Encino, Los Angeles.
"I don’t know why they are saying he's not allowed in the house," she told Fox News. "Joe is a good grandfather. The kids will tell you that."
And she has revealed that Prince Michael, Paris and Blanket are coping well following the tragic death of their dad.
"The children are doing fine," said Katherine, who has been caring for all three children since their father's passing in accordance with his will. "They're having fun."