The 21-year-old was found dead in the Humber Estuary on Wednesday afternoon and police have confirmed they are treating her death as a "potential homicide".
She had been missing since the early hours of Friday February 1 following an evening out in Hull, and her disappearance sparked an intensive search.
On Saturday, Miss Squire's mother described her family's heartache at the loss of her "darling" daughter.
In an emotional tribute, Lisa Squire affectionately referred to her daughter as "Pie" and said she had lost "one of the four most precious things in my life".Writing on Facebook, she said: "I cannot thank you enough my darling Pie for making me a mummy.
"For choosing me to be your mummy. It's an honour, a privilege and a joy.
"I kept you safe for as long as I could and I am so sorry I could not keep you safe on that night. I'm sorry. I'm so so sorry."
Mrs Squire said her lowest point was having to inform her daughter's boyfriend of her death.
In a statement issued on Friday, Detective Superintendent Martin Smalley, of Humberside Police, said: "While we have considered throughout the missing person inquiry that Libby may have come to some harm, Libby's death and the recovery of her body now leads us to solely investigate as a potential homicide."
The detective said a post-mortem examination had taken place but officers would not be releasing any results "for investigative and operational reasons".
He said: "We have to protect the integrity of the investigation, which is live and very much active and ongoing, with one man who remains under investigation."
Miss Squire, who has been described as a popular student and studied philosophy at Hull University, vanished after going out with friends on January 31.
She was dropped off in a taxi near her home in Wellesley Avenue at 11.29pm and was seen on a bench near Beverley Road around 10 minutes later.
Miss Squire is believed to have remained in this area until 12.09am the following day, February 1, but was not seen alive after that.
Her disappearance prompted a huge search effort involving more than 100 officers and a team of volunteers.
An inquest into the death will open at Hull Coroner's Court at 1pm on Monday.