Videos from the scene purported to show bystanders tackling the suspect to the ground, taking his knife and pinning him down before police intervened.
London Mayor Sadiq Khan confirmed some of those stabbed had been "seriously injured" as he applauded the "breathtaking heroism" of bystanders "who literally ran towards danger" not knowing what it was they were faced with.
London's Metropolitan Police said they were called to a stabbing near London Bridge at 1.58pm on Friday local time. Emergency services attended and a man had been detained by police.
Assistant Commissioner Neil Basu confirmed a male suspect was shot by police during the incident and died at the scene.
"A number of other people received injuries at this incident," he said, but did not confirm how many.
Basu said a wide cordon was in place for explosives, but "we believe the device that was strapped to the body of the suspect is a hoax explosive".
"Those extensive cordons will remain in place for a considerable time," he said.
Witnesses reported hearing multiple shots fired on the bridge on Friday afternoon. London Bridge was closed to traffic and cars and buses were at a standstill while a white truck lay jackknifed across the stream of traffic.
The incident comes two and a half years after the terrorist attack on London Bridge in June 2017. Eight people were killed and 48 others injured.
Video from a helicopter showed armed police swarming around the back of the truck. Other videos show a group of bystanders grappling with a person on the bridge while police surround them holding guns.
Prime Minister Boris Johnson said he was 'being kept updated' as he abandoned campaigning and rushed back to Westminster from his Uxbridge constituency.
Johnson added: "I can assure you and assure everyone that anyone involved in this attack will be hunted down and brought to justice."
It comes weeks after the UK's terror threat level was downgraded.
British Transport Police said London Bridge station, one of the city's busiest rail hubs, was closed. City of London Police, the force responsible for the business district, urged people to stay away from the area. Police boats could be seen in the River Thames directly below London Bridge.
'I was terrified'
Witnesses reported hearing gun shots during the middle of a busy Friday afternoon.
Amanda Hunter said she was on a bus when it came to a stop, saying: "There was a commotion and I looked over the window and I saw three police officers running over to a man who had something in his hand, I don't know what."
"I saw a police officer shoot him."
"I saw a man and three police officers trying to put him on the ground and then I heard about three shots go into the man and then police officers went away from the suspect."
One woman said: "I was just walking along the bridge and I heard four or five shots from behind me. I just ran. I didn't even look back. I've no idea of it was police or not. I was terrified."
People are evacuated from the area around London Bridge in central London following what has been called a terror attack. Photo / AP
Bus driver Mustafa Salih, 62, was travelling from Borough High St towards London Bridge where he saw emergency vehicles and the police cordon.
He told BBC London: "A police officer came up to me and said turn off your engine, get off and run.
"I looked up and I could see a crowd of people coming towards me. One woman was crying. I ran back down to Borough High St. It was all very scary as we did not know what was happening."
BBC reporter John McManus was in the area and said he saw figures grappling on the bridge. He said: "I thought it was initially a fight," but then shots rang out.
Guardian journalist Owen Jones said he had just cycled to the area and police were yelling "keep moving" while ushering people out from behind the cordon.
"It was a very tense atmosphere," he said. "You're in the middle of an urban area with police yelling keep moving … you know that something is very clearly off."
"I looked up and it appeared to be potentially four or five people – it looked like it was a fight.
"Then I heard someone shouting 'get back, get back'.
"People started running across the bridge and then [I] heard two gunshots and at that point obviously I ran."
Buildings in lockdown
The News UK building and others in the surrounding area have gone into lockdown. Workers from hotels in the area were seen running from the scene as buildings were evacuated.
Those in nearby buildings were told to stay inside away from the glass.
The UK's terrorism threat level was downgraded on November 4 from "severe" to "substantial", meaning attacks were thought to be "likely" rather than "highly likely".
"It shows the breath-taking heroism of members of the public who literally ran towards danger not knowing what was in front of them," he said
"Members of the public didn't know it was a hoax at the time … it shows the best of us."
Labour leader Jeremy Corbyn said: "Shocking reports from London Bridge. My thoughts are with those caught up in the incident. Thank you to the police and emergency services who are responding."
