Met Police said: 'All three were arrested on suspicion of the commission, preparation or instigation of terrorism offences under section 41 of the Terrorism Act 2000.
Police have arrested 17 so far in connection to the incident in London, but have released 12 of them without charge.
A Scotland Yard spokesman said: "Detectives investigating the London Bridge terror attack have made three more arrests and carried out two more search warrants in east London on Wednesday".
Among those also in custody are a 27-year-old man and 29-year-old man, both from Ilford, who were arrested on Wednesday night on suspicion of preparing terrorist acts.
Two men were arrested on a street in Ilford and the third was apprehended at an Ilford residence when police searched the home, authorities said. The second man, Rachid Redouane, had not aroused any suspicions.
Eight people are confirmed to have been killed in the attack on Saturday night, which was carried out by three men. Meanwhile a chair appears to be thrown in the direction of the terrorist.
Another police vehicle then arrives, and the other two terrorists can be seen getting shot - with all the action concluding in under 20 seconds. In the CCTV, the trio can be seen rushing at a passing pedestrian near Borough Market, raining down a series of blows while police cars approach.
Armed cops brought all three down eight minutes after emergency services were first called.
In a statement, they wrote: "As a family we are shocked and appalled by the actions of Khuram and his associates".
The four others known to have been killed in the attack are Londoner James McMullan, 32, Australian Kirsty Boden, 28, Canadian Chrissy Archibald, 30, and 27-year-old French national Alexandre Pigeard.