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.
Reagan Ainsley Chown, 23, faced Perth Magistrates Court on Friday after he was charged with multiple offences, including committing an act intended to prevent arrest which caused grievous bodily harm and reckless driving to escape police pursuit.
"We will be upgrading the charges to murder," Police Commissioner Col Blanch said on Monday.
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.
Mr Blanch said Const Woods would be honoured with a full police funeral, but he would speak with the officer's family about what they wanted.
"Everything is on offer for them," he said.
The commissioner went to Belmont police station on Sunday night to be with Const Woods' colleagues.
"One thing that Anthony's mum Natalie wanted was for us to celebrate his life and enjoy the person that he was and that's what we did last night," Mr Blanch said.
"There was a lot of tears, but there was a lot of laughter and that's exactly what mum and the family wanted."
The officers who were with the 28-year-old on the night will be recognised in due course, Mr Blanch said.
Flags at all police stations across the state will go to half mast.
Chown, 23, was remanded in custody to face court again on July 7.
A 20-year-old woman and 25-year-old man who allegedly were in the stolen car have been released pending further investigation.
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