Scotland Yard said Seydou Diarrassouba, 18, died of a single knife wound to the heart in the incident on Oxford Street in central London on Boxing Day.
The killing happened in front of thousands of horrified shoppers, many of them tourists, after a fight broke out between two groups of youths at a Foot Locker store.
A second man aged 21 was injured in the leg in another stabbing a few hundred metres away a few hours later.
The two incidents have revived memories of the deadly riots that rocked London and other English cities in August, when groups of masked youths looted and burned shops and five people were killed.
Police said that the 11 people arrested over the Oxford Street stabbing were all young: one was aged 16, three aged 17, five aged 19 and two aged 22.
'This all happened outside Foot Locker and inside the Foot Locker store,' senior Scotland Yard detective John Sweeney said in a televised statement on Tuesday.
'We know there were a number of people filming the incident inside Foot Locker and may have captured the incident or its aftermath and we are appealing for these people to contact us.'
Reports said Diarrassouba was of Somalian origin.
The shop remained cordoned off on Tuesday as police forensics officers worked inside. Bloodstains still marked the pavement and several bunches of flowers had been left at the police cordon.
Motti and Carly Blum, a husband and wife both aged 24, from Melbourne, who are on holiday in Europe, said they had been shopping on Oxford Street on Monday when the stabbing happened.
'It's pretty crazy that it happened in broad daylight, you wouldn't expect that here, especially with the sales and everything,' Carly Blum said.
Her husband said that by coincidence they had been in Florence, Italy earlier this month on the day when two Senegalese traders were shot.
'So yesterday it felt like this kind of stuff is happening all over Europe, although I know that you get problems everywhere. Coming from Australia you don't see this kind of thing as much,' he said.
Video footage posted on the YouTube website after Monday's stabbing showed police holding back angry youths outside the Foot Locker store while paramedics tried to revive the victim.
The outbreak of violence on the crowded thoroughfare has turned minds back to the August riots.
British authorities blamed street gangs for much of the violence and British Prime Minister David Cameron enlisted US street crime expert Bill Bratton to help find a solution.
