The four incidents happened in north, east and south London, and none are being treated as linked.
The Metropolitan Police has condemned the "senseless violence" and the small groups who chose to engage in disorder and violence" on New Year's Day.
At 11.30am on the 31st December, an 18-year-old man was stabbed in Larmans Road, Enfield, and he died in hospital that evening.
The second was at about 7.30pm, when a 20-year-old man was fatally stabbed in Memorial Avenue West Ham.
Then, at around 10.30pm, a 17-year-old male was fatally stabbed in Norwood Road near the junction with Station Rise, Tulse Hill.
Finally, at around 02:35hrs on 1 January, a 20-year-old man was fatally stabbed in Bartholomew Court, Old Street.
A second male, aged in his 20s, was taken to hospital suffering critical stab injuries.
Police have made five arrests relating to the stabbing in Enfield, but there have been no arrests yet in the other three cases.
Commander Neil Jerome, of the Met's Territorial Policing Command, said: "There were thousands of officers on duty across London yesterday and throughout the night, all determined to play their part in keeping the public safe.
"I am grateful to Londoners and visitors to the capital who co-operated with police - both at major celebrations in Westminster and at thousands of organised and private events across London - to enable the vast majority of people to enjoy New Year's Eve.
"However, there were small groups who chose to engage in disorder and violence, and whose actions have had utterly tragic consequences.
"It is heart-breaking that, at a time when so many of us are contemplating what lies ahead in 2018, four families are dealing with the grief of losing a loved one to senseless violence and the callous use of knives as lethal weapons.
"I can assure Londoners - and the families and friends of the four males killed and the fifth who remains in hospital - that detectives will work tirelessly to bring to justice those responsible for such despicable acts of violence.
"As we begin these investigations and the provision of support to four grieving families, days like this serve to re-enforce the determination of the Metropolitan Police to tackle knife crime and violence on our streets; especially offences committed by and against young people.
"I would urge anyone with information about these attacks, and more generally about anyone who routinely carries a knife, to urgently pass that information to police or Crimestoppers.
"If you've hesitated to do so before, then these four tragic deaths at the start of a new year may persuade you to act now to make London safer for your family and friends in 2018."
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