The Zambian police say Aswat was arrested on 20 July in Lusaka.
"His arrest follows ongoing security investigations on the threat of terrorism to which Mr Aswat is alleged to be connected," a statement said, signed by police inspector general Ephraim Maateyo.
"He entered the country on 6 July. He is a British national and is currently in custody of Zambian security authorities."
Meanwhile, the London bombing suspect in custody in Rome is to fight extradition to Britain, his lawyer indicated on Saturday after a preliminary extradition hearing at the Italian capital's Regina Coeli prison.
"I don't think there has been a consent to extradition on my client's part," Antonietta Sonnessa, lawyer for Osman Hussain - also known as Isaac Hamdi - told reporters outside the prison, where the 27-year-old suspect has been held since his arrest on Friday.
Lawyer Antonietta Sonnessa
leaves Rome's Regina Coeli prison
"We are in a very delicate phase," Sonnessa said. "We are really at the beginning, so no requests have been formulated yet, even on the defence's part."
The suspect was arrested on Friday at his brother's flat in Rome after fleeing London aboard a Eurostar train to Paris last Tuesday, five days after the attack on the capital's transport system.
British police are holding a total of 12 suspects in custody over the two waves of London bomb attacks.
Twenty-eight people had been arrested during the investigation into the 7 July blasts which killed 56 people, and the failed second attack on 21 July, police said.
"A total of 28 arrests have been made in the UK, of which 12 remain in police custody in connection with the investigation," London's Metropolitan Police said in a statement.
All are being held on suspicion of being behind acts of terrorism, or harbouring fugitives. Searches have taken place at 14 addresses in London and two in Britain's second city of Birmingham in central England, it said.
At least four of the alleged 21 July bombers are now held - three in London and one in Rome - but police have not confirmed reports that a fifth bomber, who dumped an unexploded device in a west London park, also had been caught.
The police in Britain are
questioning four suspects
On Friday, police swooped on a housing estate in west London, arresting two men who identified themselves as Ibrahim Muktar Said and Ramzi Mohammed.
British police are questioning the suspects to pin down any links to a wider network that they fear could strike again.
"The investigation ... is still continuing. It is dynamic and it is wide-ranging. There will be more very visible police activity," anti-terrorist police chief Peter Clarke told reporters late on Friday.
"We must not be complacent. The threat remains, and is very real," he said.
Two men arrested on Saturday under Britain's anti-terrorist law in separate pre-dawn operations in Leicester, central England, have been released without charge, police said.
They said the arrests were not connected to the July bombings in London.
"It is important to stress that there is no reason to currently suspect that these arrests are in any way connected to recent terrorist activity in London," police said in a statement.