The Hull University student was reported missing in the early hours of February 1, after a night out in the city with her friends.
Her body was recovered from the Humber Estuary six weeks after she disappeared on Wednesday, March 20.
He has since been released under investigation.
Senior Investigating Officer, Detective Superintendent Martin Smalley said: “In consultation with the Coroner, we are now in a position for Libby’s body to be released to her family.
“Libby’s parents have been informed and arrangements are being made for her to be returned to them.
“Understandably, this will be an incredibly emotional time as Libby was found just over five months ago, however for investigative reasons we were unable to return Libby back to them until now.
“I want to express my gratitude and thanks for their patience and understanding, as losing a loved one is always a heart-breaking experience, but the circumstances surrounding Libby’s tragic death make it even more devastating.
“We continue to offer our full support and I would ask people to please respect their privacy. There are no details for any funeral arrangements at this time and should this be information the family wish to share we will of course assist them however we can.
“The investigation is continuing with a file being prepared for the Crown Prosecution Service as results of the additional analysis are being finalised.”