The discovery was made on Wednesday afternoon close to Spurn Point and her remains were taken to Grimsby docks.
Squire, from High Wycombe, Buckinghamshire, was a second year religion and philosophy student. The 21-year-old was last seen just after midnight on Friday 1 February on Beverley Road close to the junction with Haworth Street in the East Yorkshire city.
Detective Superintendent Martin Smalley said: “A post-mortem examination commenced this afternoon and is continuing to be carried out this evening, however formal identification has now taken place and we can confirm the body recovered is that of missing woman Libby Squire.
“Libby’s family have been informed and are receiving support from specially trained officers.”
Smalley added: “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.”
A major operation was carried out in the days after the popular student disappeared, involving hundreds of uniformed officers as well as search specialists, dog handlers, underwater officers and the public.
Professor Susan Lea, vice-chancellor at the University of Hull, said: “As a close-knit University community of staff and students, we are all absolutely devastated by the loss of our student, Libby Squire.
“Our hearts go out to Libby’s family and friends at this incredibly difficult time and we will continue to give them our full support.
“We have been incredibly moved by the way staff, students, Humberside Police and the local community have all come together over the past few weeks.
“The kindness and care everyone has shown towards each other has been overwhelming, as has everyone’s commitment to finding Libby since she went missing.
“We will keep doing everything we can to support our staff and students as they adjust to this shocking and tragic news and we will continue to support the police fully with their investigation.
“We have provided details of the support services available to all our staff and students and ask that you please respect the privacy of Libby’s family, friends and our students by giving them space at this extremely sensitive time.”
Pawel Relowicz, 24, from Raglan Street, Hull, was arrested on suspicion of abduction in connection with her disappearance and remains under investigation.