The incident began at an event at Fishmonger's Hall at 1.58 p.m. on Friday. The suspect was shot dead by police within five minutes after being confronted by the officers, London Metropolitan Police Commissioner Cressida Dick told reporters.
"It is with the heaviest of hearts that I have to inform you that as well as the suspect, who was shot dead by police, two of those injured in this attack have tragically lost their lives," Efe news quoted Dick as saying.
"This is a very fast moving, dynamic investigation, we will keep you updated," the Commissioner said.
"In the coming days you will see more police, armed and unarmed, patrolling our streets to help reassure those who are understandably concerned," Dick said.
London's Mayor Sadiq Khan said police were not currently seeking any other individuals in connection with the attack, while hailing the "breathtaking heroism" of passers-by who wrestled with the suspect.
Video of the incident shows civil pinning the assailant to the ground and holding him until police arrived.
"A male suspect was shot by specialist armed officers from City of London Police and I can confirm that this suspect died at the scene," said Neil Basu, Assistant Commissioner for Specialist Operations.
"I am now in a position to confirm that it has been declared a terrorist incident," he said.
"We retain an open mind as to any motive."
The suspect was wearing what appeared to be a bomb vest, but proved to be "a hoax explosive device," Basu said.
The incident evoked memories of the 2017 terror attack on London Bridge when a van was deliberately driven into pedestr before its three occupants ran to the nearby Borough Market area and began stabbing people in and around restaurants and pubs, leaving eight people dead and 48 injured. The attackers, who claimed allegiance to the Islamic State, were shot dead by the police.
( With inputs from IANS )