Hannah Bladon, 21, was attacked while riding a packed tram near the Old City, as Christians celebrated Good Friday and Jews marked Passover.
The exchange student at the Hebrew University of Jerusalem was rushed to hospital but died soon after.
A police spokesman said the woman appeared to be a student visiting the city as a tourist.
Israel's national ambulance service, Magen David Adom (MDA) gave the victim's age as 25-years old.
Live images: British woman stabbed to death in Jerusalem
Fri, April 14, 2017
The woman, thought to be in her early 20s, was attacked while she travelled on a light rail train near the Old City, which was packed as Christians celebrated Good Friday and Jews marked Passover
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Israeli security forces take security measures as health team workers treat the wounded British tourist after he was attacked with a knife at a tramway in Jerusalem on April 14, 2017
Paramedics gave the victim heart massage and tried to resucitate her at the scene before taking her to Jerusalem's Haddash Hospital Mount Scopus.
She died in hospital shortly after arrival.
The Times of israel said the British Embassy in Tel Aviv was “in touch with local authorities”.
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It has been reported that the victim may have held dual citizenship.
Two other people, including a 30-year-old pregnant woman, received minor injuries in the incident on Friday morning when the tram came to an emergency stop.
The woman received treatement for a stomach injury and a 50-year-old man injured his leg.
Video footage of the alleged attacker being detained onboard the tram has been posted online.
Israel Police foreign press spokesman Micky Rosenfeld tweeted a picture of the kitchen knife said to have been used in the killing, and described the suspect as a "terrorist".
"Terrorist who carried out knife attack is from Rasal amud in his 50s. Arrested by police at the scene.," he said.
The young woman died after being stabbed repeatedly, Israeli police have said
the victim was stabbed while travelling by tram
The knife said to have been used in the attack
The area is cordoned off by police
He also told Sky News the suspect boarded the Jerusalem Light Rail at Damascus Gate, before pulling a knife out of his bag and stabbing the woman "multiple times in the upper part of the body".
The Shin Bet domestic security service said the attacker had been arrested.
They said the suspect as a 57-year-old Palestinian from Arab East Jerusalem.
The security service said the man suffered with mental health problems and had been convicted in 2011 for sexually assaulting his daughter.
It added that the assailant had previously tried to commit suicide by to swallow a razor blade.