Katie Holmes and Tom Cruise
07/09/2012 at 07:10 PM EDT
and Katie Holmes
agreed that daughter Suri should live primarily with her mother in New York with generous visitation by her father, PEOPLE has learned.
The terms of physical custody of the 6-year-old was a key element of the settlement
announced Monday just days after Holmes filed for divorce
, according to sources.
"They both love their daughter," says one source, "and Tom thinks she should be with her mother."
The superstar also "didn't want his family dragged through the mud," says the source. "Neither one of them wanted this to be hashed out in public."
Holmes has long loved New York and will enroll her daughter, who had been home-schooled by tutors, into a private school in Manhattan in the fall, according to sources.
Holmes, 33, and Suri recently moved into
a three-bedroom apartment in New York City, where the pair have been spotted out. Cruise, 50, has been at home in Los Angeles with his teenage kids, Connor, 17, and Bella, 19, before returning to work Monday on his sci-fi thriller Oblivion
Reporting by JD HEYMAN and ELIZABETH LEONARD