The 26-year-old man, named locally as Tesfa Hughes from Chapeltown, was in a Volkwagen Golf that hit an Audi A4 in Roundhay Road at the junction with Roseville Road in Harehills shortly after 7pm on Wednesday.
Police said the car was being pursued after failing to stop for a marked police BMW on Regent Street shortly before the collision.
Mr Hughes stumbled into the nearby Maureen’s Caribbean takeaway before collapsing. He was taken to Leeds General Infirmary for treatment but was pronounced dead a short time later.
The driver of the Audi, a 37-year-old woman, was also taken to hospital with injuries that are serious but not considered life threatening.
It has also emerged today that a 28-year-old pedestrian was clipped by the Golf as Mr Hughes drove along Regent Street.
The man, who was not seriously hurt, contacted police this morning and was due to be spoken to about the incident today.
Tributes have been paid on social media to Mr Hughes.
On Twitter @misslee_ said he was “genuinely one of the nicest most humble guys I have met”.
She added: “Sending all my love to his family & friends.”
Kadeena Cox said: “Getting in and scrolling through my Facebook feed has literally made my heart sink...RIP tesfa gone too early!”
Najeeba Paige wrote: “Still can’t believe it!! RIP Tesfa.”
West Yorkshire Police has appealed for witnesses to contact them and has referred the matter to the police watchdog.
Superintendent Sam Millar said: ”We are investigating the circumstances of this incident and are appealing for anyone who witnessed the incident to contact us.
“We have voluntarily referred this incident to the Independent Police Complaints Commission and currently we are working together to establish the full circumstances.”
An IPCC spokesman said: “The IPCC was referred by West Yorkshire Police a serious road traffic incident in the Harehills area of Leeds yesterday evening. The IPCC has deployed investigators to undertake an assessment. This does not amount to a formal IPCC investigation at this stage.”
Anyone who witnessed the incident or the circumstances leading up to it is asked to contact police on 101, quoting log number 1283 of May 20.