Two members of the public have died following the terror attack, and several others were injured after they were allegedly stabbed.
The suspect was shot and killed by armed officers on the bridge following the incident.
Witness Celia Sodera was on the top floor of a bus right next to the man when members of the public tackled the knife from him, then police shot him before he revealed he was wearing a suicide vest - which police have now said was a hoax.
She told Sky News: "We saw six people keeping someone on the floor.
"At one point someone said 'he has a knife'. And we thought, 'oh my god this guy was going to stab someone' because we saw people running away.
"Then the police came and finally they removed the knife, then they shot the guy.
"He was still alive and he tried to pull the black jacket off so I was able to see the vest he was wearing and it seemed like a very scary device, a bomb device.
"At that point we ran off the bus, crossing the bridge in the opposite direction. It was very scary to be honest.
"Because of the tape and the cable...it seemed like he wanted to activate the device because he was still moving after being shot.
"We were very close on the bus. That moment was horrible."
Ms Sodera added that she heard more gun shots after running off the bridge and was so scared she ran all the way to Wapping, nearly two miles away.
Jackie Bensfield, 32, said she asked to be let off another bus on the bridge after hearing "five or six" gunshots.
The nurse got off the bus and then "ran like hell" to escape the shots.
Another witness Amanda Hunter, who was also on a bus across the bridge when she heard shots fired, said: "(The bus) 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."
She told the BBC: "It seemed like there was something in his hand, I'm not 100% sure, but then one of the police officers shot him."
Footage on social media appeared to show armed officers surrounding a person on the ground before firing, while a member of the public was seen removing a large knife from the scene.
Several bystanders could be seen restraining the suspected knife attacker before police arrived.
Witness Craig Heathcote told Sky News: "I was walking across the bridge. I reached the north side and someone came running towards me saying 'get out of the way, someone's got a knife'.
"I could then see on the other side of the bridge a big scuffle of people trying to get someone to the ground.
"I just immediately called 999. There was lots of shouting and them trying to restrain him or get people out of the way before they fired the guns."
Another witness Reem Yousef said: "I was below the bridge, about 30 metres to one side of it. I heard shouting. 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."
Connor Allen, who was in his van on the bridge when it was evacuated, said: "Everyone just started running, you heard these pops and that was it. We just got out the van and started running."
Another witness wrote on Twitter: "I'm in Borough Market after shots have been heard on London Bridge. The bridge is cordoned off. The market has been evacuated.
She later posted: "Tourists are screaming, shop owners urged into their shops."
Joe, who was held in his office following the incident, told Sky News: "We saw loads of police cars heading towards the bridge. We saw a man on the ground and police pointing guns at him. We later saw a lady being carried away from the scene."
An onlooker called Zack said police officers almost knocked him over as they ran towards the incident.
"Then loads of cars with sirens all rushed past me at full speed," he said.