He was remanded in custody and will appear before Manchester Magistrates’ Court on Saturday, Greater Manchester Police said.
Michael Samwell, 35, caught thieves in the act after he went to check on a loud bang he heard with his wife in the early hours of Sunday morning.
He was struck with his black Audi S3, leaving him with severe injuries. He died after being rushed to hospital.
The thieves fled the scene and the car was found abandoned and severely damaged shortly after the incident.
A 15-year-old boy and two men aged 20 and 21 were also arrested on suspicion of murder and burglary.
They have been released on bail.
Mr Samwell trained as a naval officer at Britannia Royal Naval College in Devon and spent around a decade in the senior service before leaving in 2014.
In a tribute, his family said: “Mike's death has made a huge hole in our lives that can never be filled.
“Mike was the most wonderful husband, brother and son. He would do anything for anyone and was an ever dependable and generous family member and friend to so many. He was always smiling and sharing his amazing sense of humour. We are so proud of all that Mike was and had achieved.
“Mike was devoted to his family above anything. His wife, Jess, was his one great love above all things. He was a loyal and treasured friend. We are so grateful to have had him in our lives; he will be sorely missed by all who knew him."