Formal identification of the man who died has not yet taken place and the police said efforts were ongoing to trace his next of kin.
He had entered the water near the junction of Main Street and Ash Grove Lane, according to the force, which led to “extensive searches” involving Derbyshire Fire and Rescue Service.
The man was treated by ambulance crews at the scene before he was taken to hospital.
BBC correspondent Jeremy Ball said from the scene: “Smashed brickwork from the bridge over Egginton Brook lies in the water, below a broken ‘Welcome to the village of Egginton’ sign.
“One villager told me the road was closed until a wrecked car was removed from the bridge.”
Adrian Osiecki, 34, from Harnall Lane West in Coventry, has been charged with dangerous driving – including failing to stop for police and criminal damage to police vehicles – driving without insurance, driving while disqualified and theft of a caravan.
He is due to appear at Southern Derbyshire Magistrates’ Court on Monday.