Rapper K-Fed was said to be delighted with the surprise deal, which follows a bitter court battle.
Singer Britney, 26, will be able to visit Preston, two, and Jayden, one, Mark Vincent Kaplan said.
But Kevin, 30, will have legal and physical custody. Kaplan said the divorced couple reached a deal on Thursday.
The case was set to go to court next month.
But Kaplan said: All the issues that would have been addressed have been settled.
Kevin had not been aiming for sole custody, Kaplan said, adding: Nobody could have anticipated the turn of events that occurred.
Troubled Britney was admitted to hospital after a breakdown in January.