The name was initially published in a report by the Italian newspaper Corriere della Sera, which cited Italian intelligence sources and said that Zaghba's mother lives in the Italian city of Bologna.
Police said Zaghba is believed to be an Italian national of Moroccan dissent and was not a "police or MI5 subject of interest".
The arrest came as detectives confirmed the identity of the third terrorist involved in Saturday night's horror attacks, in which seven people died and dozens more were injured.
Commuters paused in train stations, hospital staff gathered in hospital foyers and workers stopped work in government offices at 11 a.m London time.
A woman is comforted by her friend on Tuesday as she breaks down in tears after a minute's silence in London near the scene of Saturday's terrorist attack.
A police vehicle then screeches into shot, with three armed policemen exiting and immediately trying to rescue the man by diverting his attackers' attention towards them.
"It is a heavy toll that we pay in these attacks", he added.
Butt and his two accomplices drove a hired van into pedestrians on London Bridge before stabbing people in the area around Borough Market. Twelve people who were detained in connection to the attack have been released without charge, police say.
The terrorist attack was claimed by IS but there is no evidence to suggest there was any overseas link to the planning and execution of the attack according to statements by London's Metropolitan Police.
More information emerged Tuesday about Saturday night's attack.
Le Drian said a third French citizen remained missing following the attack.
Neighbours in his east London neighbourhood of Barking said he spoke with a heavy London accent. No arrests had been made, police said.