The Alfie actor launched legal action against her upcoming book in a desperate bid to protect their children's privacy.
He wanted to block certain passages in Frost's autobiography and remove photos of his children to shield them from the glare of publicity.
However, the case was settled on Tuesday when the pair agreed terms and a judge at London's High Court granted a permanent injunction by consent.
"Sadie is getting used to Jude's fiercely protective position on anything to do with their children as he is determined to do everything he can to provide them with a normal childhood out of the glare of publicity," the Daily Star quoted a friend of the pair as saying.
"It was never Jude's intention to block the publication of the entire book. He just wanted to shield his children from the spotlight," an insider close to Law added. (ANI)