The Independent Police Complaints Commission (IPCC) said the man, named as Josh Pitt from Leighton Buzzard, died from a single gunshot wound.
He was fatally injured after police attended a property in Hibbert Street, Luton, at 14:00 GMT on 9 November.
The IPCC said body-worn video footage from some of the officers will be analysed as investigations continue.
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It said a forensic examination of the scene took place and a "a number of knives" were recovered.
A post-mortem examination on Friday gave the provisional cause of death as a gunshot wound to the chest, the IPCC said.
Mr Pitt was described by Bedfordshire Police as white and British.
He was initially treated at the scene by officers and paramedics but died at hospital at 14:50 GMT.
IPCC Commissioner Mary Cunneen said: "My thoughts and sympathies are with the family and friends of Josh and all of those affected by this fatal shooting.
"Our investigation will look at the circumstances surrounding the incident and the actions of the officers involved.
"We have spoken to Josh's next of kin to inform them of our role and will be keeping them updated.
"I ask anybody who may have seen or heard anything in the Hibbert Street area on Wednesday afternoon, which may be useful to our investigation, to contact us."

District Judge Lucy Koh's move opens the way for US sales of Samsung's older tablet model to restart.
Separately, Samsung filed a motion on Tuesday against Apple's iPhone 5 saying its patents had been violated.
The iPhone 5 was launched last month and broke Apple's pre-sales record. Apple has not commented on either move.
The South Korean firm said it had "little choice little choice but to take the steps necessary to protect our innovations and intellectual property rights".
Apple and Samsung, the two market leaders in the lucrative smartphone market, are embroiled in patent disputes in as many as 10 countries.
The ban on sales of the Galaxy Tab 10.1 in the US was put in place in June ahead of a trial.
In August, at the conclusion of that trial, Apple was awarded victory in many of its patent violation claims, centring on accusations that Samsung had copied Apple's iPhone and iPad designs. It was also awarded more than $1bn (Â£664m) in damages.
However, the jury found that Samsung had not violated the patent that was the basis for the ban on the sale of the Galaxy Tab 10.1.
Samsung, therefore, argued for the sales ban to be lifted.

Three people were left seriously injured in the incident on Marine Drive, Rhos-on-Sea, Conwy county, at about 14:25 GMT on Wednesday.
A black Citroen came off the promenade, down a grassy slope and through iron railings before rolling on to rocks.
Two adults and a teenager, all believed to be women, were taken to hospital.
An adult and teenager were airlifted to Ysbyty Gwynedd in Bangor, Gwynedd, while a second adult was taken by ambulance to Glan Clwyd Hospital, Bodelwyddan, Denbighshire.
A "number of knives" were found at the scene where a man was shot by police, investigators have said.
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A temporary sales ban on Samsung Electronics' Galaxy Tab 10.1 tablet computer in the US has been lifted by a US court.
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A woman has been arrested on suspicion of dangerous driving after a car crashed through a seafront barrier and fell on to rocks.