Amber Gibson left her home in the Hillhouse area of Hamilton, South Lanarkshire, at around 9.15pm on Friday and was reported missing later that night when she did not return.
Her body was discovered in Cadzow Glen park at around 10.10am on Sunday.
Police Scotland this evening confirmed the arrest of the 19-year-old man in connection with her death.
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It is understood the teenager was a pupil at Moore House Academy in Bathgate, West Lothian, which is privately run and cares for children aged 11 to 18.
A spokesperson from Moore House said: “Amber was a well-loved, bright and lively young girl who attended our academy in Bathgate as a day pupil.
“Our children and staff are devastated at the news of this tragedy, and we are all supporting each other through this difficult time.
“Our deepest sympathies extend to Amber’s loved ones and to everyone who knew her.”
The gates to the park and part of Cadzow Street were cordoned off on Wednesday as officers carried out investigations.
Police say that enquiries are ongoing.