Briton Tom Ballard, whose mother died on K2, was climbing Nanga Parbat in Pakistan with Italian Daniele Nardi when they lost contact on February 24.
A search operation was under way this week after four Spanish rescuers were flown to the area by military helicopter on Monday and were joined by Pakistani mountaineer Ali Sadpara at base camp.
Italian ambassador Stefano Pontecorvo said the search team has confirmed that silhouettes spotted on the mountain were the bodies of Mr Ballard and Mr Nardi.
He tweeted: “With great sadness I inform that the search for @NardiDaniele and Tom Ballard is over as @AlexTxikon and the search team have confirmed that the silhouettes spotted on Mummery at about 5900 meters are those of Daniele and Tom. R.I.P.”
He said the bodies are in a place that is difficult to reach but that everything possible will be done to try to recover them.
Mr Ballard was born in Derbyshire but moved to the Scottish Highlands in 1995, the year his mother, Alison Hargreaves, died on K2 when she was 33, months after becoming the first woman to conquer Everest unaided.
Despite being dubbed “Killer Mountain” because of its dangerous conditions, the summit of Nanga Parbat has long drawn climbers.
Located in Pakistan’s Gilgit Baltistan area, it is the ninth highest mountain in the world at 26,660ft (8,126m).
Mr Nardi and Mr Ballard set out on the climb on February 22, making it to the fourth base camp by the following day.
The pair last made contact on February 24 from an elevation of around 20,700ft (6,300m) on Nanga Parbat.
Pakistan dispatched search helicopters last week despite the closure of its airspace amid tensions with neighbouring India over the disputed Himalayan region of Kashmir.
Mr Pontecorvo said the search team involving the Spaniards this week captured photos of the silhouettes and analysis confirmed that they were the missing climbers.
Mr Nardi, 42, from near Rome, had attempted the Nanga Parbat summit in winter several times in the past.
In 2015, Mr Ballard became the first person ever to solo climb all six major north faces of the Alps in one winter.
Mr Nardi’s team posted a tribute on their offical Facebook page.
They wrote: “We’re heartbroken; we inform you that the research of Daniele and Tom has ended. A part of them will always remain on the Nanga Parbat.”
They added: “The family remembers Tom as a competent alpinist and brave friend of Daniele. Our thoughts are with him.
“Daniele will remain a husband, a father, a son, a brother and a friend lost for a dream that we have always accepted, respected and shared.
“We like to remember how you really are: in love with life, adventurous, scrupulous, courageous, loyal, attentive to detail and always present in times of need.”