The incident happened on the Ballysillan Road on Thursday morning. It is believed the woman was in her 30s and had two young children.
The man is due to appear at Belfast Magistrates’ Court this morning.
Police are appealing for information.
Superintendent Melanie Jones said, “Firstly, I would like to offer our sincere condolences to the woman’s family.
“Just after 8am on Thursday, 19 April, Police received a report that an Audi A4 car had been stolen from outside a house in the Cavehill Road area of Belfast.
“Suspecting the vehicle was still in the North Belfast area, Police Officers were deployed to search for it. Just after 10.40am, the vehicle was located by the Police Helicopter, who in adherence to strict procedures, followed the car towards Fortwilliam where it exited onto the Shore Road.
“As the car then travelled onto the Antrim road, in line with procedure designed to bring a vehicle to a controlled stop, other trained officers deployed a ’stinger’ device; however, the driver of the stolen vehicle failed to stop.
“After following at a distance, due to concerns about the dangerous manner in which the stolen car was being driven, specially trained police officers ended their pursuit, handing over to the police helicopter.
“As the stolen car travelled along the Ballysillan Road, it collided with a vehicle, before then colliding with and killing a female pedestrian.
“A 39 year old man was arrested at the scene and has been taken to Musgrave PSNI station for questioning.
“As is normal procedure, we have informed the Police Ombudsman and will fully cooperate with their investigation.
“I would like to thank those witnesses who have already come forward, but I am appealing to anyone who has any information about this incident, or who may have seen the grey Audi A4 car, registration number OFZ8287, between 6.30pm yesterday (Wednesday) evening and 10.50am this morning, to contact police on the non-emergency number 101, quoting reference 463 19/04/18.”