Constable Anthony Woods, 28, was in an induced coma at Royal Perth Hospital after the incident on Thursday but WA Police on Sunday night confirmed he had succumbed to his injuries.
"The thoughts and prayers of us all are with Anthony's family and colleagues," the force said in a statement.
Const Woods and other officers had been following the car, allegedly bearing stolen number plates, through Ascot in Perth's east about 1am on Thursday.
It came to a stop and as the officers tried to detain the three occupants, Const Woods was hit by the vehicle and dragged underneath.
Police said his fellow officers had to lift the car off him and attempted CPR at the scene before he was rushed to hospital in a critical condition.
Reagan Ainsley Chown, 23, faced Perth Magistrates Court on Friday after he was charged over the incident.
He is facing multiple offences, including committing an act intended to prevent arrest which caused grievous bodily harm and reckless driving to escape police pursuit.
He was not required to enter pleas and was remanded in custody to face court again on July 7.
Police said a 20-year-old woman and 25-year-old man who allegedly were in the stolen car had been released pending further investigation.
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