Hannah Bladon, 20 and a University of Birmingham student, has been in Jerusalem on an exchange programme at the Rothberg International School since January. She was also studying archaeology and Hebrew.
Israeli security services have said Hannah Bladon was travelling on a train when a Palestinian man pulled a knife and stabbed her repeatedly.
Police there have detained a 57-year-old man, calling him an "Arab terrorist".
The Israeli intelligence service Shin Bet added that the attacker had a history of mental illness, that he recently tried to commit suicide in hospital by swallowing a razor blade and that he was convicted of sexually abusing his daughter in 2011.
It said: "This is not the first time that a Palestinian suffering from personal, mental or moral distress has chosen to commit a terrorist attack in order to escape his problems."
President of Israel Reuven Rivlin said his country's "thoughts and prayers are with the family of the victim".
He added: "This week thousands have come through the ancient gates of Jerusalem, to celebrate the feasts of Passover and Easter throughout the city - while the security forces work to ensure the safety of the dear residents and visitors to the city.
"And so we will continue to do. Terror can never overcome us. Terror will never destroy our lives here."