Detective Inspector Gary McIntyre said: "On Thursday 16th February Cheshire Constabulary was made aware of the discovery of human remains in a well in Malia, Crete. Since then, officers have been in close liaison with the Greek authorities and have been awaiting further information.
"The remains were removed from the site and taken to a nearby hospital for further forensic examination. Tests have been carried out and we have now received confirmation from the Greek authorities that the remains belong to Steven Cook, who went missing on 1st September 2005 during a holiday to the island.
"Steven's family have been kept fully updated on the developments and are currently being supported by Cheshire officers. They have been provided with support since Steven first went missing and this will continue over the coming weeks.
"This is understandably an extremely upsetting and distressing time for the Cook family. Steven's relatives are very appreciative of all the support the media and the public have given them over the years in their quest to find him but they have asked for their privacy to be respected at this time as they are trying to come to terms with the news.
"It is important to remember that the discovery of Steven's body is being managed by the Greek authorities, who have had primacy for this case since Steven was first reported missing, and they will continue to liaise with us moving forward.
"Our priority is to ensure that Steven is flown home to the UK as soon as possible. The remains will then be subject to the Cheshire Coronial process.
"Steven was 20 at the time of his disappearance. Over the years Cheshire Constabulary has remained committed to finding him. A file on Steven’s disappearance has been maintained by the force and we always said that it will not be closed until information is received which confirms what has happened to him.
"Officers involved in Steven's case will continue to liaise with the Greek authorities, the Foreign and Commonwealth Office and Steven’s family moving forward."