Mr. McManus was captured by gunmen during a raid on his apartment in May last year.
The men were killed in Birnin-Kebbi in the north of the country
Chris McManus and Franco Lamolinara in the video made by the hostage takers.SKY NEWS
Two hostages - a Briton and an Italian - have been killed by terrorists in northern Nigeria in an attempted rescue operation.
The effort to free Chris McManus, from the North West of England, and his colleague Franco Lamolinara was launched by British special forces and the Nigerian army.
Sky sources say there were no fatalities on the British and Nigerian forces' side but there were several fatalities among the hostage-takers.
Prime Minister David Cameron said the pair appeared to have died at the hands of their captors, either before or during the course of the rescue bid.
Sky sources say it is believed there was a fight and during the assault the UK and Nigerian forces could not get to Mr McManus and Mr Lamolinara in time.
"It strongly appears that the hostage-takers shot the hostages," the sources said.
The rescue bid was launched after the UK received credible information about their whereabouts and that their lives were under increasing threat.
Speaking in Downing Street, Mr Cameron said Mr McManus and Mr Lamolinara were "taken hostage by terrorists" in northern Nigeria May last year.
He said: "Since then, we have been working closely with the Nigerian authorities to try to find Chris and Franco, and to secure their release.
"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.
"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.
"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."
He added: "Our immediate thoughts must be with Chris and Franco's families, and we offer them our sincerest condolences."
Mr McManus and Mr Lamolinara, contract workers for the construction company B Stabilini, were kidnapped by gunmen who stormed the apartment they shared in Birnin-Kebbi.
The two men were in the city building a bank.
In a statement, Mr McManus' family said: "As a family, we are of course devastated by the news of Chris' death which we received earlier today.
"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."
There have been a number of foreigners 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 and in November of the same year, four men from the US, Canada and France were taken 7.5 miles offshore on the Okoro field.
