The 21-year-old disappeared in Hull in the early hours of February 1 after an evening out.
The Hull University student's body was recovered from the Humber Estuary on March 20.
At least 250 people, including friends, family and community members, filled St Lawrence's Church in West Wycombe, Buckinghamshire, on Thursday for her funeral.
The philosophy student's coffin was taken to the church in a vintage black hearse with flowers surrounding it.
Among the flowers was a bouquet from Hull University students and staff with a card that said "rest in peace". Another bouquet had a card that read "it broke our hearts to lose you".
Her mother and father embraced as the coffin, covered with white roses, was taken into the church.
A personal tribute and poem were read by her mother Lisa during the afternoon service.
Mrs Squire also thanked friends and family for their love and support. "We would not have got through any of this without you," she told the service.
Rev Jenny Ellis conducted the service, telling the mourners: "It's a wonderful tribute for Libby and her family that so many of you are here today.
"Let's make this a wonderful celebration of a beautiful person."
Ms Ellis said the funeral was "absolutely essential" to give family, friends and the community closure.
"The whole point is to draw a line under things and enable people to move on," she told reporters after the service. "The service was about letting her go."
A video was played during the funeral showing the 21-year-old's life in photos to the tune of Phil Collins' You'll Be In My Heart and Take That's Shine.
In a post on Facebook last week, her mother asked mourners to take a photo of Miss Squire or a written memory of the 21-year-old to the service.
Miss Squire was last seen at about 12.09am on February 1 near her home on Wellesley Avenue, Hull, and was reported missing later that morning.
An intensive search was launched by hundreds of uniformed officers as well as search specialists, dog handlers, underwater officers and the public.
In March, Humberside Police confirmed that a body recovered from the Humber Estuary was that of Miss Squire.
A 25-year-old man was arrested in August on suspicion of murdering Miss Squire but was released under investigation.
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