Alice Walton, aged 20, died in hospital on Monday after being seriously hurt in the crash near Hyde Park Corner at about 4.30am on Saturday.
She was from Newark in Nottinghamshire and was a student at the University of Leeds, West Yorkshire Police have said.
She died in hospital on Monday after being seriously hurt in the crash in Woodhouse Street, near to Headingley Lane, at about 4.30am on Saturday.
“We are working with our colleagues in Nottinghamshire Police to support Alice’s family at what is clearly a very difficult time for them," said Acting Sergeant Fiona Hoodless, of West Yorkshire Police Major Collision Enquiry Team.
"The family have said they are heartbroken and devastated by their loss."
The driver of the taxi, a silver Volkswagen Passat, had stopped at the scene in Woodhouse Street, near to Headingley Lane, and was interviewed by police.
“We are continuing to carry out extensive enquiries to establish the full circumstances of the incident and would like to hear from anyone who witnessed the collision or the events leading up to it, or anyone who may have been in the area at the time in a vehicle fitted with dash-cam," said Sgt Hoodless.
“We are particularly keen to hear from anyone who saw Alice or was with her earlier in the evening.”
Anyone with information is asked to contact the Major Collision Enquiry Team on 01924 293047 or via 101 quoting Operation Padward.