Hazel North, 19, from Dunfermline in Fife, last spoke to her family on March 4 when she told her sister she was travelling to Kilmarnock to meet a friend.
Her body was found in Dean Park in the East Ayrshire town on Monday.
John Davis appeared in court yesterday 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.
A statement released by Ms North's family via police thanked people who have sent them messages of support.
The statement read: "We the family 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 at this sad time 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 from all who have spared a thought for our wee Hazel.
"We would also 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 who were involved right from the start with their excellent support at this time."