The London terrorist has been named as Khalid Masood, a 52-year-old former teacher with a string of criminal convictions, including possession of a knife.
Police said Masood was not the subject of any current investigations and there was "no prior intelligence about his intent to mount a terrorist attack".
However, he was known to police and has a range of previous convictions for assaults, including GBH, possession of offensive weapons and public order offences.
Masood was born in Kent on Christmas Day in 1964 and detectives believe he was most recently living in the West Midlands. He was also known by a number of aliases.
It is believed he was a married father-of-three, a former English teacher and a religious convert who was into bodybuilding.
Masood's first conviction was in November 1983 for criminal damage and his last in December 2003 for possession of a knife. He has not been convicted for any terrorism offences.
Earlier yesterday, British Prime Minister Theresa May disclosed that the terrorist was British-born and known to police and MI5.
He was once investigated in relation to concerns about violent extremism some years ago but was a "peripheral figure".
The case is "historic" and the attacker was "not part of the current intelligence picture", Mrs May added.
A US government source said Masood had associates with an interest in joining jihadist groups abroad, but there was no evidence he had done so himself.
As police and intelligence agencies mounted a massive investigation to piece together the killer's movements in the lead-up to the attack:
Mrs May addressed MPs as they gathered at the usual time inside the Palace of Westminster.
In a defiant message to a packed House of Commons, she said: "We will never waver in the face of terrorism."
Paying tribute to PC Keith Palmer, who died after being stabbed, she said: "He was every inch a hero and his actions will never be forgotten."
The officer's family described him as "brave and courageous", saying his friends and relatives are "shocked and devastated".
Meanwhile, Islamic State made its first public pronouncement since the atrocity, claiming in a statement: "The attacker yesterday in front of the British Parliament in London was a soldier of the Islamic State executing the operation in response to calls to target citizens of coalition nations."
Commentators pointed out the terror group has a record of opportunistically claiming attacks and said it was significant the statement did not appear to claim that it had directed the strike.
A minute's silence was held nationwide at 9.33am, including in the Palace of Westminster and at New Scotland Yard, to commemorate the four innocent people who were killed.
US president Donald Trump last night paid tribute to one of the terror attack as a "great American".
Kurt Cochran from Utah was in London celebrating his 25th wedding anniversary with his wife Melissa when the terrorist struck.
President Trump tweeted: "A great American, Kurt Cochran, was killed in the London terror attack. My prayers and condolences are with his family and friends."
Forty other people were injured in the attack, with 29 treated in hospital, where seven remained in a critical condition yesterday.
The casualties included 12 Britons, three French children, two Romanians, four South Koreans, two Greeks and one each from Germany, Poland, Ireland, China, Italy and the United States.
Three police officers were also injured, two of them seriously.
With forensic work completed, Westminster Bridge was reopened yesterday, less than 24 hours after the attack.