A number of shots were fired during the incident which happened on Shepperton Road at around 1am.
Police had sent a negotiator to the scene, following reports the man had broken into a house.
They believe the man and woman involved know each other.
In a statement, the Metropolitan Police said: “Police were called to Shepperton Road, N1 at 11pm on Thursday 4 September following reports of a man breaking into a residential address.
“Officers attended at 11.19pm and found a 40-year-old man threatening a woman with a knife.
“Due to the seriousness of the situation, a police negotiator, London Ambulance Service and firearm officers were called to the scene.
“Shortly before 1am on Friday 5 September the man was shot by police. A number of shots were fired.
“The man was treated at the scene by London Ambulance Service. He was pronounced dead on route to hospital at 1.20am.
“The woman was unharmed in the incident but is being treated for shock.”
The death comes hours after an incident in London yesterday where an 82-year-old woman was beheaded by a man in broad daylight.
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