Metropolitan Police said Masood, who was shot dead by an officer, was not the subject of any current police investigations, but had a range of previous convictions for assaults.
The 52-year-old was born in Kent and was believed to have been living in the West Midlands, BBC reports.
However, he was known to the police and his previous convictions included possession of offensive weapons and public order offences.
He had not been convicted of any terrorism offences.
Meanwhile, the Islamic State group has said it was behind the attack.
Others killed in Wednesday’s attack were Keith Palmer, Aysha Frade and American Kurt Cochran.
Already, eight arrests have been made in London and Birmingham.