Police guarding the iconic House of Commons building shot the man but several people were left with "catastrophic" injuries on Westminster Bridge, a busy traffic junction popular with tourists with views of Big Ben.
The car crashed into the railings outside the heavily guarded parliament building and witnesses described a man leaping out of the vehicle into the grounds of parliament and stabbing a police officer.
The incident comes with Europe on high alert after a series of deadly jihadist attacks and exactly a year after jihadists killed 32 people in a bomb attack in Brussels.
The parliament building was immediately sealed off and MPs and staff ordered to remain inside.
"We are treating this as a terrorist incident," police said in a statement.
Those dead included the police officer and the attacker, authorities said.
David Lidington, the British minister responsible for arranging government business, told MPs: "It seems that a police officer has been stabbed, that the alleged assailant was shot by armed police."
Prime Minister Theresa May is safe, her Downing Street office said, and was preparing to chair a meeting of the government's COBRA emergencies committee.
She was seen being driven away from parliament.
Police cordoned off a large area in Westminster and tourists on the London Eye, a popular tourist attraction, were stuck 135 metres (443 feet) in the air for around an hour during the incident.
The local Underground station at Westminster was also closed off.
- One fatality confirmed -
At least 10 patients were treated on Westminster Bridge and several hospitals were on alert, London Ambulance Service said.
French Prime Minister Bernard Cazeneuve confirmed that several French students were hurt in the attack.
US President Donald Trump said he had been briefed on the incident, describing it as "big news" and French President Francois Hollande and German Chancellor Angela Merkel expressed their condolences.
The Port of London Authority confirmed that a seriously injured woman was recovered from the River Thames, having jumped or fallen from Westminster Bridge.
"A female member of the public was recovered alive from the water, but with serious injuries," said spokesman Martin Garside.
"She has been brought ashore and is undergoing urgent medical treatment."
Polish former foreign minister Radoslaw Sikorski was in a taxi on the bridge and said a car "mowed down at least five people... one of them bleeding profusely."
Attack at parliament gates -
Pictures of what happened next showed two people being attended to on the ground inside the vehicle entrance gates of parliament.
Three shots were heard on video footage.
A staff member in parliament, who did not want to be named, told AFP: "I saw someone in dark clothing go down."
Jason Groves, the Daily Mail newspaper's political editor, said he witnessed a man coming through the vehicle entrance wielding something, heading towards a police officer, who then fell to the ground.
Another officer then shot the man from around 10 metres away "with a handgun, and then gets closer to him and shoots him again from over him and he doesn't get up".
Foreign Office minister Tobias Ellwood was pictured helping to give first aid to an injured police officer.
In Edinburgh, Scotland's parliament suspended a crucial debate and vote on whether to hold a new referendum on independence.
"The fact that our sister parliament had a serious incident is effecting this particular debate," the Edinburgh assembly's presiding officer Ken Macintosh said.
In July 2005, four British suicide bombers inspired by Al-Qaeda attacked London's transport system during rush hour, killing 52 people.
Airline security change
The incident came a day after Britain announced it planned to follow the United States and introduce a ban on electronic devices in cabins on flights from some Middle Eastern and North African countries.
Affected airlines have until Saturday to implement the measure.
US officials warned that terrorists are seeking "innovative" ways to attack airliners with smaller explosive devices hidden in consumer electronics larger than smartphones.
On Saturday, a man who had been investigated for links to radical Islam was shot dead at Paris's Orly airport after attacking a soldier on patrol and grabbing her rifle.