But the jury strongly criticised "systematic shortfalls" in Keith Larkins' healthcare, which they said "may have contributed to his behaviour".
The former security guard, who had suffered a nervous breakdown, was involved in a car chase around the airport perimeter on June 6 2003. He threatened unarmed officers with a blank-firing copy of a police-issue 8mm Glock handgun.
Armed police who were called in asked Mr Larkin several times to put down the weapon, but he continued to brandish it and attempted to steal a police vehicle. Officers and other witnesses testified that they heard Mr Larkins fire it, though the dead man's family dispute this, and ballistics tests were inconclusive.
Mr Larkins, 33, of Feltham, south-west London, died after being shot in the chest and stomach.
Commander Phil Gormley, the Metropolitan police's head of aviation security, said: "We know now that the weapon possessed by Mr Larkins was an 8mm blank-firing weapon that was an exact replica of a police Glock handgun.
"This placed the officers in the virtually impossible position of having to make an instant judgment on whether the gun was real or not.
"This incident, and its tragic outcome, only serves to highlight the dangers realistic replica firearms present, and we fully support the measures currently before parliament to ban their manufacture and sale in order to make London safer and minimise the risk of incidents such as this occurring.
"Few of us can imagine what it must be like to lose someone we love in these circumstances and on behalf of the Metropolitan police service I would like to extend my sympathy to the family of Keith Larkins.
"This has also been a stressful time for officers involved in this incident, and for their families. This verdict confirms that they acted properly, both within the law and as they have been trained to do."
The 11-strong jury, which returned a majority verdict of nine to two, said Mr Larkins' mental illness may have been misdiagnosed, resulting in lack of correct treatment.
Earlier, the dead man's mother, Maureen Larkins, told the coroner's court that her son had been receiving care in the community but she had noticed a deterioration in his mental condition in the run-up to his death, and had repeatedly urged his social worker and local mental health team to help.
Mrs Larkins told a psychiatrist who turned up at Mr Larkins' home the day he went missing: "You're too late."
The inquest had been told that Mr Larkins was displaying signs of psychosis at the time of his death.
Jurors heard that he believed he could communicate with God and that he was also obsessed with Milly Dowler, the 13-year-old girl who was murdered in Surrey in 2002.
