Officers were called to reports of vehicles being damaged in Aylesbury Road at around 10.40pm on Monday.
They found a man in his 40s had barricaded himself in a property and was making threats.
Armed officers, negotiators and other emergency services were called.
Bedfordshire Police said “despite sustained efforts over a number of hours to engage with the man and bring the incident to a safe resolution… he presented a weapon before police fired” shortly after 9.30am.
He was immediately treated at the scene but died an hour later.
Police said a cordon would stay in place for now but a number of people who were evacuated are now being helped to return.
Bedfordshire Police has referred itself to the watchdog the Independent Office for Police Conduct, a mandatory step in such a situation.
