A statement by the rescue team, which included climbers who were involved in an unsuccessful expedition with Mr Cheek earlier this year, said their search had found no sighting of the 28-year-old on Shimshal Whithorn.
The former Selkirk High School pupil had set off on his own to scale the 20,000ft peak on July 11 but has not been seen since.
It has now been accepted, by both the rescue team and his family, that Mr Cheek will likely never been found.
The rescue team searched for nine days from July 19 to July 28 and included Bruce Normand and Don Bowie, who attempted to scale Distaghil Sar North Ridge (25,00ft) with Ben.
A statement by Mr Normand said: "It is with great regret that I have to inform you of the disappearance and presumed death of our Distaghil Sar expedition colleague Ben Cheek. As you may know, Ben decided directly after the expedition, and against the advice of other members, to remain in Shimshal to attempt the north face of Shimshal Whithorn.
"He never returned from his mission.
"The most likely scenario is that he perished in an avalanche very early in his climb: there is a major avalanche cone at the base of the North face but a search of it did not find him near the surface.
The helicopter search appears to have ruled out the possibility that he climbed out of the face and was descending a different side of the mountain.
"Ground searches seem to exclude the possibility that he chose not to climb the face at all and went elsewhere.
"Ben will be sadly missed. At this time all our thoughts are with the Cheek family."
Mr Normand added that the search party had received help from the Pakistani army, British Mountaineering Council, Shimshal porters and friend Lee Harrison, who had been in the same expedition as Mr Cheek that unsuccessfully attempted to climb Shimshal Whithorn in 2006.
Mr Bowie gave a heartfelt tribute to his missing climbing colleague, who lived at Gordon before moving to Manchester a year ago.
He said: "In recollection, I very much enjoyed the days spent with Ben during our expedition to Distaghil Sar.
"Ben possessed a lightheartedness and a sense of humour that kept us all laughing and his energy and youthful spirit was always positive.
"Those days climbing with Ben will not be easily forgotten. My thoughts and prayers are with his family at this difficult time."
Laura Cheek, sister of Ben, said climbers should not feel pressurised into taking on dangerous expeditions that could see them never return.
She hoped no more families would have to endure what the Cheek family have gone through since Ben's disappearance, and cited the death of Nick Estcourt and an avalanche last month on K2, which left 11 mountaineers missing presumed dead, as other examples of climbing tragedies.
"I would ask all climbers out there to remember Ben Cheek and the men who were killed on K2," said Ms Cheek.
"The Nick Estcourt Award was set up to honour Nick Estcourt, who died in an avalanche on K2, and it was this very award that gave Ben the opportunity to go out to Pakistan.
"It is tragic that Ben has met his fate in the same way.
"An avalanche could take your life too and leave your family shattered forever.
"I can't believe that my brother will never come home again," she added.
Ms Cheek and her family have begun raising funds for SOS Children, a charity aiming to build a village for orphaned kids in northern Pakistan, in remembrance of Mr Cheek.