A statement from West Midlands Police said: "Officers from the West Midlands Counter Terrorism Unit have arrested a man in Stoke-on-Trent.
"A search warrant was conducted last night (November 30) in connection to a wider on-going review of existing licence conditions of convicted terrorism offenders.
"As a result of a search of his home address, the 34-year-old was arrested on suspicion of preparation of terrorist acts contrary to Section 5 of the Terrorism Act 2006.
"These searches continue."
The arrest came hours after prime minister Boris Johnson revealed that at least 74 convicted terrorists were out, freed on licence as the row over the early release of London Bridge attacker Usman Khan intensified.
Khan, 28, stabbed to death 25-year-old Jack Merritt and Saskia Jones, 23, in the knife rampage on Friday afternoon, leaving three other people injured.
Mr Johnson said: “What I have seen over the last 24 hours has made me angry – it’s absolutely clear that we can’t carry on with the failed approaches of the past.”
The new arrest, said West Midlands police, was not connected to London Bridge.
"There is no information to suggest that the arrested man was involved in the incident at London Bridge on Friday," it said.
"There was no immediate risk to public safety."
Khan, who was living in Stafford, struck at a conference held in Fishmongers' Hall.
He had been released from prison on licence in December 2018 and was wearing an electronic monitoring tag when he was shot dead by police after the rampage.
The 28-year-old was convicted of terror offences in February 2012 and handed an indeterminate sentence for public protection, with a minimum term of eight years, meaning he could have been kept in prison for as long he was deemed to be a threat to the public.
The sentence was quashed at the Court of Appeal in April 2013 and he was given a determinate 16-year jail term, with a five-year extended licence period, under legislation which meant he was released automatically halfway through the sentence.
Sentencing law changed later in 2012, and if Khan was given the same sentence today he would have had to serve at least two-thirds of it.