Mubashar Hussain, 29, was arrested in the Sparkbrook area of Birmingham on Sunday.
The 42-year-old traffic officer was left with potentially life-changing injuries including a broken pelvis and head, abdominal and other internal injuries after the incident in Moseley, Birmingham, the day before.
A West Midlands Police statement said: "It's alleged Mubashar Hussain hijacked a police car in Moorcroft Road, Moseley, at around 4.45pm and reversed into the officer, knocking him down, before driving over his body as he lay pinned under the vehicle.
"The 29-year-old, formerly of Sherwood Road in Hall Green, was arrested yesterday in the Sparkbrook area and has now been charged with a catalogue of offences, including attempted murder of the 42-year-old traffic cop.
"He also faces charges of causing serious injury by dangerous driving, a separate count of dangerous driving, wounding another officer who suffered a cut arm, four counts of assaulting other PCs, driving while disqualified, motoring offences and two car thefts.
"The car thefts relate to a Range Rover Sport stolen at around 4.30pm on Saturday and another Range Rover stolen in Birmingham the previous day.
"A second man, 24-year-old Ahsan Ghafoor, from Fulham Road in Sparkhill, has been charged with the same two car thefts, plus dangerous driving and other motoring offences.
"Both are set to appear at Birmingham Magistrates Court tomorrow (12 August)."
The injured officer was due to undergo further surgery on Sunday.
Superintendant Tom Joyce said: "It's difficult to give a prognosis at the moment. They are certainly potentially life-changing - but we are relieved to say, we understand they are not believed to be life-threatening.
"His wife is aware of the incident and is with him at this time."
The officer has been with West Midlands Police for 17 years, and worked as a traffic officer for the last 12 of those, and Supt Joyce said his father had also been a police officer.