An appeal to unseal the rest of the documents was made by the Miami Herald newspaper, which has run investigations into Epstein. It was rejected three times.
But last month the United States Court of Appeals for the Second Circuit ordered their release, ruling that the public's right to know outweighed the privacy rights of the individuals named.
In what may be an indication of the fame of those individuals, the judges made a striking plea to the media to "exercise restraint" in reporting the allegations about to come to light. They also allowed parties involved to apply for minor redactions, delaying the release.
Another delay is possible as Maxwell has launched an appeal to keep the documents sealed, her lawyers arguing that a full release would trigger a "furious feeding frenzy".
They wrote: "Plaintiff Giuffre made numerous allegations of sexual, if not criminal, conduct against a wide range of third parties. Because of the media no reference to anyone in this case is benign: A reference to any person is toxic and lethal to that person's reputation. Facts and truth are all but irrelevant."
The legal battle between Giuffre and Maxwell began in 2014 when Giuffre claimed Epstein sexually abused her starting in 2000 when she was 16, with the "assistance and participation" of Maxwell.
She also made allegations against the Duke of York, which were categorically denied by Buckingham Palace.
Maxwell described the claims as "obvious lies", and Giuffre then sued her for defamation.
The appeal court's decision to release the documents came just three days before Epstein was arrested last month, charged with sex trafficking.
Prosecutors in New York have accused him of assaulting girls as young as 14.