Lauren, who is pregnant with Cowell's child, finalised proceedings in New York Civil Court on Wednesday, reported E! online.
Both Lauren and Andrew also reportedly agreed to joint custody over their seven-year-old son, who will primarily live in New York City.
Lauren is expected to celebrate the news by throwing a baby shower this weekend.
In August this year, Lauren had said in a statement. "I am committed to sorting things out with Andrew as amicably as possible to ensure the well-being of our son, I would hope for some space and privacy in order to work through this."