Chris McManus, 28, was shot six times through a toilet door just as the joint raid by British special forces and Nigerian troops authorised by British Prime Minister David Cameron began in March 2012.
Special forces came under AK-47 fire from the kidnappers as they attempted to carry out the mission at the compound in the city of Sokoto in north-west Nigeria, the hearing was told.
A post-mortem examination found that McManus died from a single gunshot wound to the head that killed him almost instantly.
Friendly fire was ruled out in the death because the rescue forces were using different ammunition from that which killed the Briton.
Italian engineer Franco Lamolinara, 48, was also killed before the rescue could be successfully carried out.
The coroner David Ridley recorded a verdict of unlawful killing at the end of the hearing in Salisbury, southwest England.
The family of McManus said in a statement that they accepted that the decisions taken by the authorities who organised the attempted rescue “were the only ones possible based on the information available.”
“We hoped until the end for a positive outcome as we are sure did Chris and Franco,” the statement said.
“They were always in a dangerous situation from the time of their kidnapping. However, the sequence of events particularly over the last few days of their lives, played out in such a manner as to make it a hopeless one.”
The failed operation caused a diplomatic row between Britain and Italy at the time after Italian president Giorgio Napolitano said it was “inexplicable” that Downing Street had not alerted Rome to the plan to rescue the men in advance.
But British Foreign Secretary William Hague had insisted it had been impossible to inform the Italian authorities in advance.
McManus had been working as a quantity surveyor for Italian-owned construction company B.Stabilini when he was captured by gunmen who stormed his apartment near Sokoto in May 2011.
British officials at the time blamed a splinter wing of the Boko Haram sect for the abductions, but the group denied involvement.
Lamolinara was also abducted and a Nigerian engineer was shot and wounded but a German colleague managed to escape by scaling a wall.
A video released later showed the kidnappers claiming they belonged to Al-Qaeda and threatening to kill McManus and Lamolinara if their demands were not met.
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