A four-day search for the missing student ended in the early hours yesterday when police uncovered human remains near Milngavie, to the north of the city, six miles from where she used to live.
A man is expected to be charged in connection with her death when he appears in court today.
He is understood to be Alexander Pacteau, 21, who was helping police with their inquiries earlier this week.
Detective Superintendent Jim Kerr, who is leading the investigation, confirmed at a press conference that the body was that of Miss Buckley.
He said: “I can now confirm that the body found by officers at the farm in north Glasgow is that of Karen Buckley.
“We cannot imagine the pain and suffering of Karen’s family and friends and all our thoughts are with them at this very sad and distressing time.”
In a statement, Miss Buckley’s father, John, said he and his wife Marian had lost a daughter who was “cherished” by her family.
The statement read: “Marian and I, together with our sons Brendan, Kieran and Damian, are absolutely heartbroken. Karen was our only daughter, cherished by her family and loved by her friends.
“She was an outgoing girl who travelled the world where she met lots of people and thoroughly enjoyed her life. We will miss her terribly.”
Police have said Miss Buckley’s friends raised the alarm on Sunday after she failed to return from a night out at the Sanctuary club in Glasgow.
She had told friends she was going to the toilet at around 1am but failed to return and did not take her jacket with her.
On Monday, police traced a man seen with the student on CCTV after she left the nightclub. The following day her handbag was discovered in Dawsholm Park, in the north-west of the city.
Police dogs, divers and a helicopter crew were all involved in the hunt for the student.
The search eventually led police to High Craigton Farm on the north-western outskirts of Glasgow where human remains were recovered.
On Facebook yesterday, Miss Buckley’s friend Julie Malone described her as an “intelligent, kind, beautiful” girl.
She wrote: “There are so many broken hearts today for you Karen. If there is one thing your friends and family can do for you now [it] is to remember you for you, the intelligent, kind, beautiful, happy girl we all know and love and not for this last week.
“My life is richer that you have been in it Karen and you will be forever in my heart. I love you forever Buckaroo, my little Karebear. I miss you more than anyone could ever imagine.”
Another friend Aoife Dooley wrote: “We will always love you and miss you forever Karen.”
Last night nearly £50,000 had been raised as part of a 24-hour appeal to help her family. The online fund was set up by the student’s former nursing classmates from Limerick University. A spokeswoman for the university said the community, and in particular the department of nursing and midwifery, was deeply saddened by what had happened.
“Karen was a very valued member of the UL community as well as the wider nursing and medical communities in Limerick, having spent time working in both the University Hospital Limerick and the University Maternity Hospital,” she said.
“The thoughts of the entire UL community are with her parents and family and her wide circle of friends.”
Father Joe O’Keeffe, parish priest of Mourneabbey in north Cork, described the deep sense of despair in the area where the Buckley family live.
“All we can say to the parishioners is to pray for the Buckley family and to continue to keep them in our prayers,” Father O’Keeffe said.
“We are there for the family in solidarity with them and hopefully continue to be in the days that lie ahead. I suppose we were living in hope of better news.”
Miss Buckley moved to Scotland in February and was a first-year occupational therapy student at Glasgow Caledonian University (GCU).
First Minister Nicola Sturgeon was among those passing her support to the Buckley family yesterday, while Ireland’s minister for foreign affairs Charlie Flanagan said: “All of our thoughts and prayers are with Karen’s parents, John and Marian, and with all of her family and friends at this tragic time.
“On behalf of the government, I wish to express appreciation for all that has been done by the Scottish authorities, and especially Police Scotland in Glasgow, to find Karen and to support the Buckley family throughout this very difficult time.”
Professor Pamela Gillies, principal GCU, said: “Our community is deeply saddened by the news of the loss of our student Karen Buckley.
“On behalf of all of us at the university, I offer my sincere condolences to her parents, family, friends and classmates.
“It is so tragic to lose someone so young and talented in such difficult circumstances.
“Karen’s lecturers describe her as a lovely young women, who was conscientious and a good team player, popular with her peers, and looking forward to a successful career in occupational therapy.”
The Glasgow nightclub where Miss Buckley was last seen alive by her friends closed for the evening last night as a mark of respect.
A message on its Facebook page said: “Heartbreaking news about Karen Buckley, our thoughts are with all her family and friends at this difficult time.
“As a mark of respect for Karen, we will not be opening the Sanctuary tonight. RIP Karen.”
In Ireland, Joan Burton, the Irish deputy prime minister, told parliament her thoughts were with the grieving parents and her three brothers.
“It’s every parent’s nightmare what has unfolded in recent days,” she said.
As messages poured in, the University of Limerick held a mass in her memory and created a small memorial with a photograph and candle at the reception to the health sciences building where Miss Buckley’s nursing studies began.
Northern Ireland’s deputy first minister Martin McGuinness said the discovery was heartbreakingly sad.
The Irish Nurses’ and Midwives’ Organisation also offered sympathy to Miss Buckley’s family, friends and nursing colleagues on behalf of all its members.
“Her family and her former colleagues in University Hospital Limerick are in our thoughts and prayers at this very difficult time,” the union said.
Sean Sherlock, a junior minister from the Cork area, added: “My thoughts and prayers are with the family and friends of Karen in Mourneabbey, Cork, Glasgow and throughout the world.”
St Mary’s Secondary School in Mallow, Cork, where Miss Buckley had been a pupil before going to college, also expressed its sympathies for her family.
SCOTSMAN TABLET AND MOBILE APPS