Rifat Mehmet is accused of being among a group of three fake officers who tricked their way into the house in Hawthorn Close, in Bordesley, in the early hours of Wednesday, January 20.
The 55-year-old was arrested near the A14 in Northamptonshire at around 2.15am.
On Wednesday night, he was charged with impersonating a police officer, robbery, driving without insurance, dangerous driving and aggravated vehicle taking.
Mehmet, from Charlecote Road in Dagenham, Essex, was set to appear before Birmingham Magistrates Court on Thursday.
Detectives from West Midlands Police are continuing to appeal for witnesses to the robbery which occurred just before 1.30am on Wednesday.
A spokesman for the force said: "We believe a petite white woman, aged in her early 20s, and a black man were involved in the deception and robbery.
"If anyone saw people dressed in police uniform in Hawthorn Close or surrounding roads, or people acting suspiciously, we would urge them to get in touch.
"We would also ask motorists in the area at the time to check dash-cam footage to see if it shows a black Ford Focus – registration MT13 NWZ – driving away from the scene. We believe it was likely to be in tandem with another vehicle."
Anyone with information can call West Midlands Police on 101.