Jeshma Raithatha, studying for A-Level (equivalent to SSC) was reported missing from her family home in Greenford, west London, since Monday last week.
Her body was found hidden in bushes at the edge of the park on Tuesday, they said.
Jeshma, who planned to go to university but also cherished ambitions to be a professional singer, was last seen May 16 by a staff member at Claremont High School in Kenton, west London, where she was a sixth-form pupil.
According to the police, she failed to return home on that day and was reported missing by her parents, Suresh and Manjula Raithatha. She would have turned 18 last Thursday and had been due to appear for her first A-Level exam on Monday.
"Although a formal identification is yet to take place, officers believe the body to be that of missing person Jeshma Raithatha, aged 18. The death is being treated as murder. An open mind is being kept as regards the motive," said Scotland Yard.
Jeshma's family said her disappearance was "completely out of character" and described her as a happy young woman.
"Jeshma was in a happy state and was looking forward to her life," said her mother, who also has a 15-year-old son and a 12-year-old daughter.