The Duke of Sussex wrote about the "sex crimes" allegations in his new memoir "Spare," which officially came out on Tuesday.
The lawyers sent a document to Judge Lewis A. Kaplan that would dismiss the August lawsuit once he signs it.
The Duke of York has just settled the high-profile case out of court after months of back and forth.
The two parties reached an out-of-court settlement, according to a notice filed on Tuesday.
The former Duke of York has strenuously denied Giuffre’s allegations, and attempted to get the lawsuit tossed.
His father, Prince Charles, did the same thing a few days ago.
Virginia Giuffre filed the lawsuit against the royal in August.
The deal between Epstein and Virginia Roberts, now known as Virginia Giuffre, contained a paragraph that said it protects anyone “who could have been included as a potential defendant” from lawsuits filed by Giuffre.
Attorneys for both Prince Andrew and Virginia Giuffre said they expected to depose eight to 12 individuals.
The document is a 2008 settlement agreement that the Prince's lawyer says would protect him against claims that he sexually abused an American when she was 17.