Katherine will become the legal guardian of Prince Michael, 12, and Paris, 11 - the two children he had with Debbie – and will also get custody of seven-year-old Blanket, whose biological mother has never been named.
The agreement, in which Debbie will have visitation rights with the two oldest children and will continue to receive spousal support payments, will be finalised in a court hearing on Monday in Los Angeles.
Her legal representative said the parties had "engaged in a dignified discussion that resulted in a dignified outcome".
Katherine's lawyers added: "Mrs Jackson and the family are pleased this matter is resolved and was handled in a caring, thoughtful and courteous manner.
"We were all united in our goals to do what is best for Michael's wonderful children, and both Mrs Jackson and Debbie Rowe were on the exact same page."
Katherine was named in Michael's will as his choice of carer for his children, should anything happen to him. She was granted temporary custody after his June 25 death.
As the investigation into the Thriller singer's death continues, the Los Angeles County Coroner's office have said the release of his autopsy results has been delayed until next week.