Larossi Abballa, 25, was well known to French police.
He was arrested in 2011 and sentenced in 2013 to two-and-a-half years in jail for recruiting jihadists to fight in Pakistan.
Witnesses said he shouted "allahu akbar" (God is great) as he launched his knife attacks on policeman Jean-Baptiste S. The victim's partner, fellow police official Jessica S, was later stabbed to death inside the couple's home.
The killer declared allegiance to jihadist group Islamic State in a long video posted on Facebook's live site. Pictures of his two victims were posted, according to David Thomson, a French specialist on militant Islam who saw the video before the account was suspended.
Chillingly, Mr Thomson said Abballa could he heard deciding what to do with the couple's son. The killer also refers to the European football championship currently taking place in France, declaring that "the Euros will be a graveyard".
On his computer, said police sources, was a list of figures Abballa wished to target, including two in the public eye.
Former anti-terror judge Marc Trevidic, who questioned Abballa after his 2011 arrest, said that he was one of a group of people. Two of the men had travelled to the Pakistani city of Lahore to meet a local al-Qaeda figure but were immediately arrested the moment they arrived at the airport.
At the time Abballa was a relatively minor figure, he told Le Figaro (in French). "He wanted to carry out jihad [holy war], for sure. He had been in training in France, not militarily but physically."
The leader of the eight-member group, an Indian national, was given eight years in jail and banned from French territory while six others were given lesser sentences. Abballa was jailed for three years, of which six months were suspended, with another two years of probation.
In an article from the time of his trial, Le Monde quotes him as describing himself as rudderless - and radicalised by the internet.
"I needed recognition, I didn't work and I had just failed to pass my CAP [professional qualification]. They started talking to me about religion, which I found comforting."
He went on to describe the "group effect".
"We talked only of jihad," he said. "It's like someone who lives 24 hours a day with thieves. Automatically, he too will become a thief!
"When I watched videos about the oppression of Muslims, they had such an effect on me...it was too moving. Then, it only needed a few words, and I was gone."
On release from prison he was placed on France's "S-list" of individuals seen as a danger to state security.
Abballa had reportedly been the subject of a recent anti-terrorist investigation into a Syrian jihadist group, including having his phone tapped, but that apparently did not yield sufficient evidence to merit his arrest.
A few months ago, he set up a night-time fast-food service called Dr Food which made deliveries between 22:30 and 05:00.
The delivery service featured on his Facebook page, which was suspended on Tuesday morning.
His last entry, at 05:03 (03:03 GMT) on Monday, featured a photo-montage including the Euro 2016 logo, a crucifixion and the Masonic emblem of a square and compasses, under a caption that read: "And some will say people see evil everywhere!"