The attempt to free engineers Chris McManus, from the north-west of England, and Franco Lamolinara was launched by Nigerian forces with UK assistance.
The family of Mr McManus said last night that they were “devastated” by his death.
Prime Minister David Cameron said both men appeared to have died at the hands of their captors, either before or during the course of the rescue bid.
It was launched after the UK received “credible information” about the hostages’ whereabouts, Mr Cameron said.
The Prime Minister authorised the mission as it was believed their lives were under increasing threat.
Mr Cameron said: “Early indications are clear that both men were murdered by their captors, before they could be rescued.
“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.”
Mr McManus was seized in northern Nigeria in May last year and was believed to have been held by a splinter group of Muslim terrorists Boko Haram, which has potential links to al-Qaeda.
Last night, his parents spoke of their shock at the news.
“As a family, we are of course devastated by the news of Chris’s death,” they said in a statement.
“During this ordeal we have relied heavily on the support of our family and friends which has never waned and has enabled us to get through the most difficult of times.
“We are also aware of the many people who were working to try and have Chris returned to our family, and his girlfriend. We would like to thank all of them for their efforts. We knew Chris was in an extremely dangerous situation. However, we knew that everything that could be done was being done.”
They added: “We now need time to grieve and come to terms with our loss.”
Labour leader Ed Miliband said: “Our hearts go out to the families of Chris McManus and Franco Lamolinara.
“Their murder is a horrific event. I condemn unreservedly the callous cruelty of their kidnappers and we pay tribute to those who risked their lives in attempting to rescue them.”
The Italian government said Mr Cameron had phoned his Italian counterpart to give him the news. Both victims were engineers working for Italian construction company B Stabilini.
Mr McManus, a contract worker, was kidnapped by a “horde of gunmen” in May last year. Raiders stormed his apartment in Birnin Kebbi, in the north west of the country, and captured him along with Mr Lamolinara.
A German colleague managed to escape by scaling a wall but a Nigerian engineer was shot and wounded in the raid. The men were in the city building a bank.
The Foreign and Commonwealth Office (FCO) said last night the men were killed in Sokoto, Sokoto State, to the north-east of the city they had been taken from.
In December last year a Nigerian group calling itself “al-Qaeda in the land beyond the Sahil” announced it had captured Mr McManus.
It released a hostage video claiming it had kidnapped the Briton and showed a blindfolded and bearded man in an orange vest. Three men in dark clothing stood behind him armed with rifles and a machete.
It was reported the man pictured in the video called for the British government to respond to the demands of the group, so they would spare his life.
A number of foreigners have been kidnapped while working in Nigeria in recent years.
In September 2008 two Britons were held by the Movement for the Emancipation of Niger Delta. A Scottish oil worker was abducted and his guard killed in April 2009, in the Rivers State capital Port Harcourt.
Three Britons and a Colombian were kidnapped in January 2010. In November 2010 four men from the US, Canada and France were taken 7.5 miles offshore on the Okoro field.
In January last year two French hostages were kidnapped from Niamey, the capital of neighbouring Niger to Nigeria’s north.