Humberside Police had been carrying out extensive searches for the 21-year-old after she disappeared near her Hull home after a night out.
Detective Superintendent Martin Smalley said formal identification has now taken place after the body was found on Wednesday afternoon.
He said: “Libby’s family have been informed and are receiving support from specially trained officers. We would ask their privacy is please respected at this incredibly distressing time.
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"The people in Hull have shown tremendous support to Libby’s family and to the officers and support staff involved in the searches and investigation.
"It has been a very difficult time for all those involved and we would like to thank everyone once again for their support.
“One man was arrested in February in connection to Libby’s disappearance and remains under investigation.
“We will provide updates as and when we can as to the progress of the investigation, which has been continuous since Libby’s disappearance and remains ongoing.
“Our priority is to support Libby’s family and give them the answers they desperately need.”
The last known sighting of the University of Hull philosophy student, originally from High Wycombe, Buckinghamshire, was just after midnight on Friday February 1 at the junction of Beverley Road and Haworth Street in Hull.
Last week, marking six weeks since she went missing, video footage of the happy and smiling student singing along in a car with her family was released as they said they miss her "beyond belief".