Laurent Bonomo, 23, was stabbed almost 200 times with up to 100 injuries inflicted after he was already dead, sources said.
His close friend, Gabriel Ferez, 23, suffered around 50 injuries during a long ordeal at his friend's bedsit in south-east London.
Sources said both men were unable to move after being bound and gagged some time before 10pm on Sunday.
Investigators believe a flammable liquid was poured on or near their bodies, possibly in an attempt to destroy evidence.
The two young men are believed to have been playing a computer game together when they were attacked by one or more men in Sterling Gardens, New Cross.
Detectives believe a burglary at the rented flat six days earlier could be linked to the double murder.
They said there was no evidence of forced entry and a set of keys may have been used, enabling an attacker to surprise his victims.
Neighbour Christina Ramires, 32, from Brazil, said she arrived home five minutes after the bang.
She said she saw the bodies being taken to the ambulance.
Her Spanish friend, also a neighbour, reportedly told her that she saw two men banging on the window of the flat prior to a "very strong sound", which she took for an explosion of some kind.
Mrs Ramires, who is a journalist by trade, said when she arrived she could see through the open door of the flat which was blackened and greasy.
She said she did not know the resident of the flat by name but she saw a man and a woman cooking in the ground floor kitchen almost every day.
She said trouble in the area was rare but their flat had been broken into three or four months ago, before they moved in.
The one-bedroom ground floor flat of a three-storey terraced block is situated in a pleasant cul-de-sac in a relatively leafy part of New Cross.
Police have cordoned off the flat, with scaffolding and tarpaulins erected across the downstairs bay window and kitchen window.
A police officer stood guard at the entrance to the block.
Detectives said Mr Bonomo, of Velaux, and Mr Ferez, of Prouzel, were "entirely innocent", with no criminal background in France or the UK.
The bio-engineering students were due to return home later this month after a three-month placement at Imperial College London.
Detective Chief Inspector Mick Duthie told a press conference at New Scotland Yard: "I have never seen injuries inflicted to bodies like this before."
He said: "The extent of the injuries are horrific. Everyone working on this case, including myself, has been deeply shocked by what we have seen.
"I have never seen injuries like this throughout my career. We are here today because I don't know why these boys were killed or who killed them.
"I do believe, however, that those responsible must have been blood-stained when they left."
The detective said no weapon has been recovered during extensive searches in the area and both men must have suffered a lengthy ordeal.
Mr Duthie said police are hunting a white man seen running from the flats shortly after the explosion. But they have not ruled out that others may have been involved.
Mr Duthie said both victims were found lying in the living area of the ground-floor bedsit. There was a strong smell of an accelerant used to ignite the fire.
Mr Duthie said forensic examinations were at an early stage at the "extremely complex scene", which was left in disarray.
He said investigators did not yet know if anything was missing but a break-in took place six days earlier in which a laptop was taken.
Asked if it was a case of mistaken identity, Mr Duthie said: "That is one line of inquiry.
"We cannot find anything in these two young men's background to suggest they were involved in any criminality, that they had done anything wrong. They were here as students."
The detective said Mr Ferez, who lived at another south London address, was visiting his close friend Mr Bonomo when the attack took place.
Asked to describe the attack, he said: "I would not say this was a professional attack. I would say it was a frenzied, horrible, horrific attack.
"I imagine it would take some considerable amount of time to inflict the nature of the injuries."
Mr Duthie said Mr Bonomo was known to be alive in the early hours of Sunday morning because he spoke to his girlfriend.
Detectives are studying some "limited" CCTV footage recorded in the area around Sterling Gardens on Sunday night.
The students were spending the summer working on research in Imperial College's life sciences department.
Imperial Rector Sir Roy Anderson expressed his shock and sadness at the news.
He said: "Our immediate thoughts are with their families. Laurent and Gabriel had bright futures ahead of them and it is dreadful that their lives should end so soon.
"I would also like to offer my support to the Imperial community as we mourn the loss of two young members.
"We offer our sympathies to those who knew and worked with Laurent and Gabriel. We are thinking of you during this very difficult time."
The pair were studying on Imperial's research opportunities programme, which allows students who have not yet graduated from their Masters degree to take part in real research.
Student Nicky Crowhurst, 25, who shared a laboratory with Mr Ferez in the biochemistry building, said he was a "really nice guy".
"It's a huge shock. I can't believe it. Him and his mate were always in the lab. They had only been here a little while. He was a quiet guy but really friendly."
Professor Steve Matthews, who worked closely with Mr Bonomo, said he was an intelligent young man with a bright future.
He said the keen chess player had fitted in quickly and made friends in the department.
He said: "They were both very likeable chaps. Laurent was particularly mature and well-rounded. He was a keen tennis fan and looking forward to following the French players at Wimbledon.
"We are all stunned and shocked, to say the least. Our thoughts are with their families and Laurent's girlfriend."
He went on: "Laurent was very well-liked. He was intelligent and he obviously had a bright future. He was conspicuous in the fact that he was mature, well-rounded and with excellent English."
A university spokesman said Mr Bonomo was studying a parasite which can spread from cats to human foetuses.
Mr Ferez's research was into bacteria which create ethanol for use as fuel.
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