The London Bridge attacker has been named as
Metropolitan Police Assistant Commissioner Neil Basu said 28-year-old Khan had been living in the Staffordshire area and officers were searching the address.
He added police were "not actively seeking anyone else" over the attack, which left a man and a woman dead.
In a statement, Basu said: "We are now in a position to confirm the identity of the suspect as 28-year-old Usman Khan, who had been residing in the Staffordshire area.
"As a result, officers are, tonight, carrying out searches at an address in Staffordshire.
"This individual was known to authorities, having been convicted in 2012 for terrorism offences.
"He was released from prison in December 2018 on licence and clearly, a key line of enquiry now is to establish how he came to carry out this attack."
Khan was wearing a fake suicide vest on Friday afternoon in full view of horrified onlookers.
Three people - a man and two women - were also injured in the rampage and are being treated in hospital, Basu said.
In February 2012, Khan was ordered to serve at least eight years in prison over his part in an al Qaida-inspired terror group that plotted to bomb the London Stock Exchange and build a terrorist training camp on land in Pakistan-controlled Kashmir owned by Khan's family.
The Stoke-on-Trent-based radical, along with two co-conspirators, originally received an indeterminate sentence for public protection but this was quashed at the Court of Appeal in April 2013 and he was given a determinate 16-year jail term.
Prime Minister Boris Johnson, whose party has been in power for the past nine years, said he had "long argued" that it is a "mistake to allow serious and violent criminals to come out of prison early and it is very important that we get out of that habit and that we enforce the appropriate sentences for dangerous criminals, especially for terrorists, that I think the public will want to see".
The Times newspaper reported that Khan was attending a conference on prisoner rehabilitation organised by University of Cambridge-associated Learning Together at Fishmongers' Hall and "threatened to blow up" the building.
Professor Stephen Toope, Vice-Chancellor of the University of Cambridge, said he was "devastated" that an event organised by its Institute of Criminology was targeted in the attack.
He said: "I am devastated to learn that today's hateful attack on London Bridge may have been targeted at staff, students and alumni attending an event organised by the University of Cambridge's Institute of Criminology.
"We are in touch with the Metropolitan Police, and awaiting further details of the victims.
"We mourn the dead and we hope for a speedy recovery for the injured. Our thoughts are with all their families and friends."
