Jonathan Havron, 18, who was studying uniformed services at the college near Beverley, went missing in the early hours of Saturday, February 27.
His body was found in the basin of the River Foss earlier today.
Mr Havron, of Huntington, was last seen at the Lowther Arms on Cumberland Street in York.
Inspector Mark Henderson, of York Police, said: “I can confirm that the body of the young man found in the River Foss earlier today has been formally identified by his family as that of the missing York teenager Jonathan Havron.
“Our thoughts are with the family and I ask that they be left alone at this particularly difficult time.
“Although there are no suspicious circumstances surrounding his disappearance we are still trying to establish how Jonathan came to be in the river.”