Brighton-based Nicola Brookes uploaded a supportive post on the social network about The X Factor's Frankie Cocozza, and was then targeted by abuse.
The High Court has granted her an order that will force Facebook to reveal the IP addresses of the cyber bullies.
Brookes was falsely called a paedophile and drug dealer, by anonymous users. She also claimed a fake profile was created in her name, which sent explicit messages to girls.
She plans to bring a private prosecution against the abusers.
In a statement, Facebook said: "There is no place for harassment on Facebook, but unfortunately a small minority of malicious individuals exist online, just as they do offline. We respect our legal obligations and work with law enforcement to ensure that such people are brought to justice."
Brookes' solicitor Rupinder Bains confirmed Facebook did not contest the order.