PM David Cameron, speaking at No 10, said he had authorised the rescue mission in a bid to save Brit Chris McManus.
He was kidnapped in May 2011 in the north of the country alongside an Italian colleague Franco Lamolinara.
Mr Cameron said the Government had received information on their location and that their lives were in imminent danger.
He said: "We are still awaiting confirmation of the details, but the early indications are clear that both men were murdered by their captors, before they could be rescued."
The mission was carried out by Nigerian forces with the assistance of Britain's Special Boat Service, it was claimed.
Both men were working for an Italian building firm when they were snatched in Bernin Kebbi by a group which later identified itself as "al-Qaeda in the land beyond the Sahil".
They were later seen in video footage blindfolded in front of their heavily armed captors.
Mr Cameron added: "The terrorists holding the two hostages made very clear threats to take their lives, including in a video that was posted on the internet.
"After months of not knowing where they were being held, we received credible information about their location.
"A window of opportunity arose to secure their release. We also had reason to believe that their lives were under imminent and growing danger.
Elite force ... Special Boat Service
"Preparations were made to mount an operation to attempt to rescue Chris and Franco. Together with the Nigerian Government, today I authorised it to go ahead, with UK support.
"It is with great regret that I have to say that both Chris and Franco have lost their lives."
He revealed he had spoken to Mr McManus's family since the failed mission.
He said: "Our immediate thoughts must be with Chris and Franco's families, and we offer them our sincerest condolences.
"Both families have endured a terrible ordeal, and this is a devastating moment for all of them.
"The Foreign Office have been in regular contact with the McManus family since Chris's capture. I spoke to them just before Christmas and I have spoken to them again with the news this afternoon.
"I want to take this opportunity to thank the Nigerian authorities, and President Jonathan personally, for all they have done to help find Chris, and combat terrorism.
"I also want to pay tribute to all those, including UK personnel, who worked so hard to try to bring Chris home safely. I am very sorry that this ended so tragically."
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