Hazel North, 19, from Dunfermline in Fife, last spoke to her sister on March 4, telling her she was travelling to meet a friend 60 miles away in Kilmarnock.
Her remains were discovered in the East Ayrshire town's Dean Park.
Police Scotland said a 25-year-old man has been arrested and is currently in custody over the death. He has not been named, but is due to appear before Kilmarnock Sheriff Court tomorrow.
The statement said: "We can confirm that a 25-year-old man has been arrested and is presently detained in police custody in connection with her death. A report will be submitted to the Procurator Fiscal."
The news came hours after police made an appeal for information at a press conference.
Chief Superintendent Gillian MacDonald, from Police Scotland's Ayrshire division, said: "Officers have carried out a detailed search and excavation of an area within Dean Park and the body of a young woman has been found.
"We believe this to be Hazel North. Hazel's family has been advised of this and officers are supporting them at this difficult time.
"A full forensic examination of the site remains ongoing and a post-mortem examination will take place tomorrow to establish the exact cause of death.
"I can confirm that a number of people have been spoken to in connection with the inquiry into Hazel's disappearance and these inquiries are very much ongoing."
Forensic teams previously searched a flat and garden in Kilmarnock's Northcraig Road in the hunt for Ms North, from the Cairneyhill area of Dunfermline.
Officers have also been investigating a possible sighting on March 18 in Stranraer, Dumfries and Galloway, where the teenager used to live.
They are examining a report that she was seen in the town's Coronation Drive in the company of another woman.
Anyone with information is asked to contact police on 101.