Masood, 52, was born in Kent and detectives believe he was most recently living in the West Midlands. Masood was also known by a number of aliases, Scotland Yard says.
Masood was not the subject of any current investigations and there was no prior intelligence about his intent to mount a terrorist attack.
He was known to police, however, and had a range of previous convictions for assaults, including GBH, possession of offensive weapons and public order offenses.
His first conviction was in November 1983 for criminal damage and his last conviction was in December 2003 for possession of a knife.
He had never been convicted for any terrorism offences, police say.
Masood killed three and injured 29 people in a terrorist attack in Westminster on Wednesday. He rammed pedestrians while speeding across Westminster Bridge in a car, then ran towards Parliament and stabbed a police officer dead.
Masood was shot dead by an armed police officer outside Parliament.
Giving details of the attacker’s background in Parliament today, May said the assailant was known to police and MI5 – the UK’s domestic intelligence agency.
“What I can confirm is that the man was British-born and that – some years ago – he was once investigated in relation to concerns about violent extremism. He was a peripheral figure.
“The case is historic – he was not part of the current intelligence picture. There was no prior intelligence of his intent – or of the plot. Intensive investigations continue.”
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