Officers were called to Duck Lane, St Neots, Cambridgeshire, after concerns for the safety of people inside were reported on Wednesday evening.
The man, named locally as married father-of-three Richard Davies, was shot by a firearms officer about 15 minutes later and died at the scene.
The Independent Police Complaints Commission (IPCC) is investigating.
A spokesman for the watchdog said the man's next of kin had been informed and the area would remain cordoned off "for some time" while IPCC investigations took place.
Cambridgeshire Police said it would "not be appropriate to comment further" at this stage, but said it was the first time firearms officers have shot someone dead in the county.
No-one else was injured in the incident.
Mr Davies, a fitter believed to have been in his 40s, was described as a friendly family man by neighbours.
He worked for mechanical engineering firm Bosch Rexroth in nearby Cromwell Road.
A spokesman said the company was "saddened" but could not comment further as there was an ongoing investigation.
Residents reported hearing raised voices shortly before the police arrived at the house.
One said: "There was definitely some kind of row last night. We heard shouting for a few minutes then it seemed to die down."
Another neighbour, who did not want to be named, said: "I heard three loud bangs and thought they were fireworks."
Resident Mary Bath, 65, said:  "We heard the bangs and joked it sounded like gunfire. Suddenly there were police everywhere and we realised it was serious."
A man has been shot dead by police after officers were called to a house in Cambridgeshire.