The 73-year-old pedestrian suffered a serious head injury in the crash near Bond Street station in front of horrified shoppers at 4.30pm on Tuesday.
The cyclist stopped at the scene and was arrested after police checks showed he was wanted in connection with an unrelated alleged offence involving criminal damage, standard.co.uk said.
The woman was taken to a central London hospital following the crash, but died in the early hours of Wednesday morning.
A video has since emerged of the cyclist arguing with officers as he is arrested for the alleged unrelated offence.
He can be seen shouting to the officers trying to restrain him: “You’re breaking my arm, what are you holding me for? You are trying to make a show of me. That’s what police do.”
Witnesses told the Standard they saw two cyclists turning onto Oxford Street before one struck the elderly woman.
Roads in the area were closed for several hours following the incident, reopening at 8.30pm.
Antonio Mendoca, 61, was handing out newspapers in Bond Street station at the time of the incident.
He said: “Everyone ran towards her to see if they could help. One guy tried to pick her up and get her out of the middle of the road but others stopped him.
“There were so many people around and they helped stop the traffic. The police came and took over.”
A Met Police spokesman said: “Police were called at 4:29pmon Tuesday, September 12 to reports of a road traffic collision on Oxford Street.
"At the scene, officers discovered a cyclist in collision with a pedestrian.
“The pedestrian, a 73-year-old woman, was taken to a central London hospital with a head injury. She died in the early hours of Wednesday, 13 September.
“Next of kin have been informed.”
No arrests have been made in relation to the collision.
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