Lauren and Andrew Silverman Reach 'Amicable' Divorce Settlement
updated 08/14/2013 AT 04:45 PM EDT
•originally published 08/14/2013 AT 03:30 PM EDT
Just two days after a source told PEOPLE that The X Factor judge, 53, "won't see Lauren in person until things calm down" with her and estranged husband Andrew Silverman, PEOPLE confirms that the exes reached an "amicable" divorce settlement in New York on Wednesday.
"As I've said all along, my priority was resolving this quickly for the sake of our son," Silverman tells PEOPLE in a statement. "Lauren and I both love him very much and I'm looking forward to starting a new chapter in our lives. Hopefully people will respect our family's privacy."
"The matter has been resolved and the parties have moved on," Lauren's attorneys, Robert S. Cohen and Bernard Clair say in a statement.
The split is expected to be finalized in the coming days, a source tells PEOPLE.
Cowell is expecting a child with Lauren, 36, who wasn't separated at the time the baby was conceived.
The music connoisseur recently distanced himself from the drama and went on vacation, where he was "happy," according to the first source, who also said Simon cares about Lauren "and has been checking in on her and the baby."