He's a Moroccan-Italian who is reported to have been stopped at an airport in Italy on suspicion that he was bound for Syria. London's Metropolitan Police Service said 22-year-old Zaghba was not a "person of interest" before Saturday's attack.
Media reports in Italy however said Italian authorities had alerted their British counterparts about his movements. The Italian newspaper Corriere della Serra said Zaghba was stopped at a Bologna airport in 2016 with a one-way ticket to Istanbul.
London police earlier admitted that one of the other two attackers, Khuram Shazad Butt, was on their radar as a member of the outlawed radical Islamist group al-Muhajiroun, co-founded by notorious hate preacher Anjem Choudary.
Seven people died and 48 were injured when the three men rammed a van into pedestrians on London Bridge before launching a stabbing spree in bars and restaurants at nearby Borough Market on Saturday night.