The Met Police has declared the attack a terrorist incident.
The suspect, who died at the scene, was believed to have been wearing a hoax explosive device, police said.
A BBC reporter at the scene said he had seen a fight on the bridge, with several men restraining one man. Police then arrived quickly and a number of shots were fired at him, he said.
Details are still emerging and Neil Basu, the head of UK counter-terrorism policing, said the force was keeping an open mind over the motive.
