The man was pronounced dead shortly before 10:30, the police said, adding that the force had made a mandatory referral to the Independent Office for Police Conduct.
A spokesperson said armed officers arrived in Aylesbury Road after reports of “a concern for welfare for a man at a property in Bedford”.
Officers were supported at the scene by police negotiators, the East of England Ambulance Service, two critical care crews from Magpas Air Ambulance and Bedfordshire Fire and Rescue Service.
The man’s next of kin are being supported by specialist officers, the force said.
Police moved residents of about 10 houses to safety during the operation and told other people living nearby to stay inside.
They were able to return when the emergency services deemed there was no “ongoing risk to the public”.
