A letter filed to the US district court on Tuesday said the Duke of York and Ms Giuffre had reached an out-of-court settlement.
She had previously claimed Andrew sexually assaulted her on three occasions when she was 17, allegations he has repeatedly denied.
The letter added that the Duke "never intended to malign Ms Giuffre's character" and that he recognised she had "suffered both as an established victim of abuse and as a result of unfair public attacks".
