One of the attackers Rachid Redouane is believed to have lived in Dublin
The announcement is a sign the investigation has reached a stage where the police can be confident of revealing hitherto secret details.
The Metropolitan police said Khuram Shazad Butt was a British citizen who was born in Pakistan, while Rachid Redouane, who claimed to be Moroccan and Libyan, also used the name Rachid Elkhdar, with a different date of birth of 3/7/91.
Redouane is thought to have settled in Dublin about five years ago where he worked as a pastry chef. It's also thought that he spent time here as recently as three months ago.
Assistant Commissioner Mark Rowley said in a statement: "I would urge anyone with information about these men, their movements in the days and hours before the attack and the places they frequented to come forward.
"The police and our partners are doing everything we can across the country to help prevent further attacks and protect the public from harm.
"At any one time MI5 and police are conducting around 500 active investigations, involving 3,000 subjects of interest. Additionally, there are around 20,000 individuals who are former subjects of interest, whose risk remains subject to review by MI5 and its partners."
Earlier today it was confirmed that an Irish identity card was found on one of the attackers who was shot dead by police.
"An Garda Síochána is providing every assistance to our colleagues in the London Metropolitan Police in relation to the terror attack in London,” the force said in a statement.
"We will process all requests from the UK authorities in relation to enquiries into individuals, identities or any other matter.”
Additional reporting from IRN.