A man armed with a meat tenderiser and a hammer who threatened police has been shot dead in Sydney's south after a taser failed to slow him down.

The incident occurred just before 12.40am on Monday after police were called to a Rockdale street over concerns for the 51-year-old man's welfare.

He had some hours earlier left a property in Brighton-Le-Sands acting erratically.

NSW Police searched nearby bushland before the fatal confrontation, with the man dying at the scene despite attempts by paramedics to save him.

Assistant Commissioner Mick Willing said the incident occurred in seconds and had been caught on body cam footage by an attending officer.

"I'm advised he also eventually ran at police officers armed with a meat tenderiser and a hammer - officers attempted to taser the man, that was unsuccessful before an officer fired a single shot which struck the man," Mr Willing told reporters on Monday.

The incident will now be subject to a review and has been referred to the NSW coroner.