The body of Hazel North was found in Kilmarnock's Dean Park town on Monday. She had last spoken to her family on March 4 when she told her sister she was travelling to the East Ayrshire town to meet a friend.
Last night, they released a statement saying they would always remember her "fun-loving smile and energetic personality" and thanked people who have sent them messages of support.
The statement read: "We are devastated by the tragic loss of our beautiful wee Hazel, who was so suddenly taken away from us.
"No words can ever express our feelings and although we will never see her mature into a beautiful woman, we will always remember her fun-loving smile and energetic personality.
"We take comfort from all the sincere messages of sympathy.
"We would like to thank everyone who has shown their concern at this inconsolable time for us. The family thanks the police for all their man hours, effort and professionalism.
"We would also like to thank the family liaison officers with their excellent support."
The 19-year-old had attended Stranraer Academy before moving to Dunfermline several years ago with her father Graham and her siblings. Her mother Rosina still lives in the west coast town.
In January, Ms North had told friends on Facebook: "2014 looks like it's gonna be my year. Love life at the moment, got everything I want and need!"
After she was reported missing, police initially focused their search in Kilmarnock. The search then moved to Kilmarnock's Dean Castle Country Park at the weekend, leading to her remains being discovered. Her body was taken to Southern General Hospital in Glasgow for a post-mortem examination.
l John Davis appeared in court on Tuesday accused of murdering Ms North. The 25-year-old, from Kilmarnock, made no plea or declaration at the town's sheriff court and was remanded in custody. He is also accused of assault and attempting to defeat the ends of justice.