Kent-born Masood, who died in the attack, was not the subject of any current police investigations, but had a range of previous convictions.
The 52-year-old was believed to have been living in the West Midlands.
The so-called Islamic State group has said it was behind the attack, in which PC Keith Palmer, Aysha Frade and US tourist Kurt Cochran were killed.
Masood drove into pedestrians on Westminster Bridge before crashing his car into railings and then running into the grounds of Parliament, armed with a knife. He stabbed PC Palmer and then was shot dead.