Police shot dead the man, who had strapped a fake bomb to his body before stabbing a number of people, in what they said was a terrorism incident.
Videos on social media showed a crowd of people who had tackled the man to the ground, before being moved away by police who then shot him.
"I ... want pay tribute to the extraordinary bravery of those members of the public who physically intervened to protect the lives of others," Prime Minister Boris Johnson said. "For me they represent the very best of our country and I thank them on behalf of all of our country."
London Mayor Sadiq Khan said those who confronted the attacker would not have known that a bomb device strapped to his body was a hoax.
"What's remarkable about the images we've seen is the breath-taking heroism of members of the public who literally ran towards danger not knowing what confronted them," Khan told reporters.
"They really are the best of us," he added.
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In the videos, a man can be seen retrieving a knife from the melee on the ground before urging bystanders to get away.
George Robarts, a translator who was on the bridge at the time, said the unidentified man had run through traffic and jumped the central partition to tackle the attacker with several people.
"We ran away but looks like he disarmed him," he said in a tweet. "Amazing bravery."
Other Twitter users praised the man seen removing the knife. One said he should have his mortgage waived and another said he should never have to buy a drink again.
Rob Underwood, a 65-year-old from Lincolnshire, eastern England, who was visiting London for the day, said he heard bangs that sounded like a firecracker going off and did not initially realize they were gunshots.
"Once you see everybody rushing and scattering, you (are) really fearing for your own safety and I think the major thing was just to get out of the way and get down," he told Reuters.
"You just feel very scared, very anxious about what's happening and just wait for whatever is going to pass."