A major police search was launched when Karen Buckley was reported missing by friends in April when she failed to return after leaving a nightclub in Glasgow’s west end.
The 24-year-old’s body was found at High Craigton Farm on the north-western outskirts of the city following a four-day search.
Alexander Pacteau, 21, has appeared in court charged with her murder.
Miss Buckley’s parents, John and Marian, travelled to Scotland after she disappeared and said they were touched by the support they had received.
In a statement issued through the Irish Examiner newspaper, Mr Buckley said: “We are very grateful for all the support and messages of sympathy we received from so many people from all over Scotland at this terrible time for our family.
“People have been extremely helpful to us right from the moment we discovered that Karen was missing.
“We would like to thank everybody in Scotland who helped us in any way.
“People have been very good to us and it means a lot. The Scottish police were wonderful and very professional right through it all, and we really appreciated that Detective Inspector Alan Burton and Sergeants Hannah Naseem and Elaine Carey took the trouble to travel to Ireland for Karen’s funeral.
“It was a very kind and thoughtful thing to do.”
Miss Buckley’s case touched many people in both Scotland and Ireland, with a number of memorial services held for her.
Around 300 people attended a vigil in Glasgow’s George Square in April, including her parents.
Miss Buckley, a qualified nurse, moved to Scotland in February and was studying occupational therapy at Glasgow Caledonian University.
Mr Buckley said: “We will never forget the huge outpouring of support and sympathy we got when we were in Scotland – it was incredible.
“We want to thank everybody who took part in the search for Karen and the hundreds of people who turned out for the vigil in George Square.
“We are extremely upset that Karen will never have the chance to live out her life, travel more and pursue her career in occupational therapy, that maybe someday she could have a family of her own and enjoy a happy and eventful life, which is what she would have wanted.
“We are still in shock and disbelief and it sometimes feels like all of this isn’t real.”
Pacteau is also accused of attempting to defeat the ends of justice.
He made no plea or declaration when he made his second appearance at Glasgow Sheriff Court in April and was remanded in custody.