Christie Brinkley will retain sole custody of her children after reaching a settlement in her ugly divorce battle with ex Peter Cook, the New York Post reports.

The agreement came around 6:15 a.m. Thursday after overnight negotiations.

A source tells the Post that Cook, 49, will continue their current custody arrangement: He will get their kids, Jack, 13, and Sailor, 10, every Wednesday and alternating weekends, plus alternating weeks during the summer.

Brinkley, 54 -- who will keep all 18 properties in the Hamptons that were being disputed -- also agreed to pay him $2.1 million.

"I am very happy with the settlement," Brinkley told Access Hollywoodas she entered court Thursday. "Didn't sleep a wink. It's a great day."

[usm]