The Metropolitan Police said "a number" of people were wounded but gave no information on how many or their conditions. London Mayor Sadiq Khan said some of the injured were in serious condition.
Khan said police weren't looking for anyone else, and Prime Minister Boris Johnson said that "to the best of our knowledge, the incident has been contained."
Metropolitan Police counterterrorism chief Neil Basu said the suspect appeared to be wearing a bomb vest but it turned out to be "a hoax explosive device."
Basu said officers were keeping "an open mind as to any motive."
The violence erupted two-and-a-half years after a van and knife attack in the same area killed eight people.
Police said a stabbing at a "premises" near the pedestrian and vehicle bridge, which links the city's business district with the south bank of the River Thames, was reported about 2 p.m.
Minutes later, witnesses saw a knifeman being wrestled to the ground by members of the public on the bridge before armed-response officers shot him dead.
One video posted on social media showed two men struggling on the bridge before police pulled a man in civilian clothes off a black-clad man on the ground. Gunshots followed. Another depicted a man in suit and overcoat holding a long knife that apparently had been taken from the attacker.
Other images showed police, guns drawn, pointing at a figure on the ground in the distance.
Karen Bosch, who was on a bus crossing the bridge, said she saw police "wrestling with one tall, bearded man" and then heard "gunshots, two loud pops."
She said the man "pulled his coat back which showed that he had some sort of vest underneath, whether it's a stab vest, or some sort of explosive vest, the police then really quickly moved backwards, away."
Another bus passenger, Amanda Hunter, told the BBC that the vehicle "all of a sudden stopped and there was commotion and I looked out the window and I just saw these three police officers going over to a man."
"It seemed like there was something in his hand, I'm not 100% sure, but then one of the police officers shot him."
Police confirmed that the man died at the scene.
The mayor praised the "breathtaking heroism of members of the public who literally ran towards danger not knowing what confronted him."
"They are the best of us," Khan said.
The prime minister also praised the bystanders, and said anyone who was involved in the attack "will be hunted down and will be brought to justice."
Cars and buses on the busy bridge were at a standstill after the shooting, with a white truck stopped diagonally across the lanes. Video footage showed police pointing guns at the truck before moving to check its container.
British Transport Police said London Bridge station, one of the city's busiest rail hubs, was closed and trains were not stopping there.
Scores of police, some armed with submachine guns, flooded the area, ushering office workers and tourists out of the area, which is packed with office buildings, banks, restaurants and bars. Staff in nearby office blocks were told to stay inside.
As police cleared the streets, staff in shops and restaurants ushered customers into storerooms and basements. Some had been through similar traumatic events: In June 2017, eight people died in a van and knife attack in the same area.
In that attack, three assailants inspired by the Islamic State group ran down people on the bridge, killing two, before stabbing several people to death in nearby Borough Market.
The 2017 fatal attack took place days before a general election. Britons are due to go to the polls again on Dec. 12.
Political leaders expressed shock and sorrow at Friday's attack. Johnson suspended his election campaigning for the day after the attack and said he would be "reviewing the matter in the course of the next few hours."
In March 2017, an attacker killed four people with a car on nearby Westminster Bridge then fatally stabbed a police officer before security forces shot and killed him in a courtyard outside Parliament.
Security officials earlier this month downgraded Britain's terrorism threat level from "severe" to "substantial," which means an attack is seen as "likely" rather than "highly likely." The assessment was made by the Joint Terrorism Analysis Centre, an independent expert body that evaluates intelligence, terrorist capability and intentions.
The U.K.'s terror threat was last listed as "substantial" in August 2014; since then it has held steady at "severe," briefly rising to "critical" in May and September 2017.