The other two victims, both women, who were taken to the hospital suffered injuries that did not appear to be life-threatening, investigators said.
Deputy Assistant Commissioner Lucy D’Orsi said the suspect wore what turned out to be a “hoax device” strapped to his body during the stabbing.
Gulled Bulhan, a 19-year-old student from Streatham, told Sky News that he was crossing the road when he saw the suspect being chased while wearing "silver canisters."
"I saw a man with a machete and silver canisters on his chest being chased by what I assume was an undercover police officer -- as they were in civilian clothing," he told Sky News. "The man was then shot. I think I heard three gunshots but I can't quite remember."
D’Orsi said the investigation is being led by officers with London Metropolitan Police’s Counter Terrorism Command.
“The incident was quickly declared as a terrorist incident and we believe it to be Islamist-related,” she said. “However as you would expect, officers continue to work in the area to ensure there is no continuing danger to the public and that all evidence is gathered.”
Police said the scene was fully contained by 4 p.m. local time.
Officials with the U.S. Embassy in London said they were aware of the situation and asked people to avoid the area.