They were identified as Khuram Shazad Butt and Rachid Redouane, both residents of London. Police and MI5 - the UK's counterintelligence and security agency - were familiar with him, but there was no intelligence to suggest the weekend attack was being planned, police said.
Butt, 27, was born in Pakistan and Redouane, 30, claimed to be Moroccan and Libyan.
The two names were announced are allegedly responsible for the killing of seven people and injuring 48 others on Saturday.
Police have not identified the third attacker.
Labour Party leader Jeremy Corbyn said he supported those calling for May to resign because of her role reducing police staffing during her tenure as home secretary, though he said the best remedy was to vote her out.
Seven people were killed in the assault, which occurred Saturday when three masked men drove a van into pedestrians on the bridge before jumping out and stabbing people at random.
During that time, police numbers have dropped by roughly 20,000 officers, and the number of armed officers has fallen as well. Trump tweeted Sunday. Khan had told Londoners there was no "reason to be alarmed" by an increased police presence, and said of the terrorists, "we will never let them win".
The three assailants were all shot dead by responding officers less than eight minutes after they were first called.
Earlier today, the police had arrested 12 people in connection to the terror attack - third in the three months in the United Kingdom.
The "terrorists" on Saturday rammed a white van onto pedestrians on London Bridge on Saturday.
Pressure on May intensified when she faced a volley of questions over police cuts from journalists at a campaign event. "She had room in her heart for everyone and believed strongly that every person was to be valued and respected", said her family, who live in Castlegar in British Columbia, in a statement.
Metropolitan Police Commissioner Cressida Dick said Monday that the country needed to rethink police resourcing and strategy.
May defended her government's stance on the issue, saying that her Conservative government had protected police budgets.
Jeremy Corbyn, leader of the main opposition party, called on May to resign over the issue, saying earlier that "you can not protect the public on the cheap", and promising to recruit another 10,000 police officers if he is elected into power.
In an update on the victims of the violence that started on London Bridge and continued in Borough Market, officials said Monday that of the 48 people who were taken to the hospital, "36 are now being cared for in London hospitals with 18 remaining in a critical condition". Nearly all are from Barking, where at least two of the attackers lived.
ISIS said its "soldiers" carried out the attack. "One whole day", she said.
The Islamic State terror group, also known as Daesh, has claimed responsibility for the London Bridge rampage, while the attack has sparked fears Britain is in the grip of a spate of copycat incidents.
One unnamed man told BBC one of the attackers had become more extreme over the past two years.
Details of the investigation had been kept closely under wraps, in stark contrast to last month's Manchester bombing, when photos and information from the investigation were repeatedly leaked to the U.S. media, triggering a row between the British and American governments.
Rachid is believed to be the attacker who was carrying an ID card issued in Ireland when he was shot dead. "He was standing over there, I could see them from my window", Gasperri said.