Richard Davies, 41, died of a single gunshot wound to the chest after shooting at officers in St Neots, Cambridgeshire, in October 2015.
A firearms officer told the inquest in Peterborough he shot at the father-of-three fearing he was about to kill.
Jurors heard Mr Davies "wanted to end his life" due to his marriage ending.
Assistant Chief Constable Paul Fullwood from Cambridgeshire Police said thoughts were "with the family of Mr Davies at what must be an extremely distressing time".
ACC Fullwood said: "Our firearms officers have an exceptionally difficult job and they are often faced with extremely dangerous situations when there is a threat to the life of others and themselves.
"No officer wants to take a life and making the decision to shoot someone in a complex and dangerous situation is extremely difficult but something officers in the role know they could be required to do."
The inquest was told Mr Davies had been drinking and tied up his children at the house in Duck Lane before they managed to escape and call 999.
The firearms officer, referred to as I7, said he heard a bang as his police car arrived and saw Mr Davies fire a shot from an upstairs window.
"I believed he had already shot at police and I believed he was about to do it again," I7 told the jury.
"Believing there was an immediate threat, I aimed at the centre of what I could see, which was the middle of his chest, and fired one shot to try and stop him firing again.
Another officer told the hearing that a Taser and baton gun would not have been effective as Mr Davies was inside the property and too far away from them.
The Independent Police Complaints Commission said a gun and two knives were found inside the home.
A man who was shot dead by police after taking his children hostage was lawfully killed, an inquest jury has decided.