Coulibaly died in a hail of bullets along with four hostages in the storming of the Jewish supermarket.
But Boumeddiene may have eluded capture during the confusion as the hostages were running away, police said.
The couple 'married' in a religious ceremony after Boumedienne, who was never seen without her veil, waited four years for him to come out of jail following his conviction for armed robbery.
The couple were never married in a civil ceremony - the only marriage legally accepted in France.
While Coulibaly had a well documented track record, Boumeddiene tonight remains a shadowy figure.
French police named the hostage taker as Amedy Coulibaly (left), 32, while also claiming a woman named Hayat Boumeddiene (right), 26, is involved. Photo / AP
But it's becoming clear that the one-time cashier was radicalised after meeting the man she would marry.
She told police who interviewed her as part of their inquiries into Coulibaly's murky dealings with Islamic extremists that she had walked away from a job as a cashier in 2009 and taken the veil.
'When I saw the massacre of the innocents in Palestine, in Iraq, in Chetchna, in Afghanistan or anywhere the Americans sent their bombers, all that...well, who are the terrorists?'
She added that when Americans killed innocents, it was the right of men to defend their women and children.
Always cool and composed, Boumeddiene never wavered under police cross examination.
When told that they knew she and Coulbaly had visited Beghal at the same time as Cherif Kouachi and two other convicted terrorists, jihadi recruiter Ahmed Laidouni, and Farid Melouk of GIA, she replied: 'We went there for crossbow practice.'
To neighbours the pair were quiet, respectful and normal and had even gone on a holiday to Malaysia together.
But a month ago they simply disappeared from their suburban house until flashed across the world's screens today.
Coulibaly murdered at least four hostages at the Kosher supermarket in Paris, according to Reuters news agency.
He is believed to be part of an Al Qaeda terror cell linked to a British-based jihadi extremist, Djamel Beghal.
Like Cherif Kouachi, who carried out the Charlie Hebdo attack, Coulibay was mentored by the key al Qaeda leader who recruited terrorists while worshipping at London's Finsbury Park mosque.
Coulibaly and Kouachi met the 50-year-old Beghal, once accused of being Osama bin Laden's main European recruiter, while in prison in Paris.
They maintained links with the Al Qaeda lynchpin after being released from jail in 2009.
As part of a jihadist cell with Said and Cherif Kouachi, he was involved in the failed prison-break attempt of Smain Ait Ali Belkacem, the mastermind behind a wave of bombings in France in 1995 which killed eight people and wounded 120.
The suspected kidnapper and killer has a long history of both petty and serious crimes. The only boy born in a family of ten in Juvisy, Essonne, he first came to police attention as a 17-year-old delinquent.
Convictions for theft and drug offences followed. In September 2002 in Orleans, Loiret, he was arrested for the armed robbery of a bank.
It's believed he became involved with the younger of the Kouachi brothers, Cherif, when he was part of a jihadist recruitment ring in Paris that sent fighters to join the conflict in Iraq. Kouachi was subsequently sentenced to three years in prison.
It is not known whether Boumeddiene was in the Kosher store with Coulibaly.
The two sieges by suspected Islamic terrorists played out at the same time, as fears grew that they would be looking to cause another bloodbath.
Coulibaly is believed to be the one responsible for shooting a policewoman dead in south Paris on Thursday.
The revelation led police to link it to the murder of 12 people around the offices of the Charlie Hebdo satirical magazine on Wednesday.
'He was in the same Buttes Chaumount cell as the Kouachi brothers,' said a source close to the investigation.
'He was friends of both of them.'
Both Said Kouachi, 34, and his brother, Cherif Kouachi, 32 - who have been killed in a building north of Paris - were first arrested in 2005
Suspects: The three men were named as Cherif Kouachi (left), 32, his brother Said Kouachi (right), 34, and Hamyd Mourad, 18, of Gennevilliers. Photo / AP
They were suspected members of the Buttes Chaumont - a group operating out of the 19th arrondissement of Paris and sending terrorist fighters to Iraq.
Cherif was convicted in 2008 to three years in prison, with 18 months suspended, for his association with the underground organisation.
He had wanted to fly to Iraq via Syria, and was found with a manual for a Kalashnikov - the automatic weapon used in Wednesday's attack.
Said was freed after questioning by police, but - like his brother - was known to have been radicalised after the Iraq War of 2003, when Anglo-American forces deposed Saddam Hussein.
Both brothers were said to be infuriated by the killing of Muslims by western soldiers and war planes.
Vincent Olliviers, Cherif's lawyer at the time, described him as initially being an 'apprentice loser - a delivery boy in a cap who smoked hashish and delivered pizzas to buy his drugs.
But Mr Ollivier said the 'clueless kid who did not know what to do with his life met people who gave him the feeling of being important'.
Belkacem was a leading members of the GIA, or Armed Islamic Army - an Algerian terror outfit responsible for numerous atrocities.
The Kouachi brothers, who are orphans, were radicalised by an Iman operating in northern Paris.
They were raised in foster care in Rennes, in western France, with Cherif training as a fitness instructor before moving to Paris.
They lived in the 19th arrondissement and were radicalised by Farid Benyettou, a janitor-turned-preacher who gave sermons calling for jihad in Iraq and suicide bombings.
The Kouachis share similar backgrounds to Mohammed Merah, the 23-year-old French Algerian responsible for murdering seven people, including four Jews and three Muslim soldiers, in the Toulouse area in 2012.
Merah, who was himself shot dead by police, had also been left to operate as a terrorist in France, despite the authorities knowing he had trained with Al Qaeda in Afghanistan.
- Daily Mail
