The breach was revealed by security researchers Charlie Miller, a former staffer at the NSA, and Chris Valasek.
• How hackers took over my computer
• Hackers can unlock your car with little more than a laptop
They worked with Andy Greenberg, a writer with tech website Wired.com, who drove the Jeep Cherokee on public roads in St Louis, Missouri.
In his disturbing account Greenberg described how the air vents started blasting out cold air and the radio came on full blast when the hack began.
The windscreen wipers turned on with wiper fluid, blurring the glass, and a picture of the two hackers appeared on the car’s digital display to signify they had gained access.
Greenberg said that the hackers then slowed the car to a halt just as he was getting on the highway, causing a tailback behind him – though it got worse after that.
Greenberg wrote: ‘The most disturbing maneuver came when they cut the Jeep’s brakes, leaving me frantically pumping the pedal as the 2-ton SUV slid uncontrollably into a ditch.
‘The researchers say they’re working on perfecting their steering control – for now they can only hijack the wheel when the Jeep is in reverse.
‘Their hack enables surveillance too: They can track a targeted Jeep’s GPS coordinates, measure its speed, and even drop pins on a map to trace its route.’
The hack was possible thanks to Uconnect, the Internet connected computer feature that has been installed in fleets of Fiat Chrysler cars since late 2013.
It controls the entertainment system, deals with navigation and allows phone calls.
The feature also allows owners to start the car remotely, flash the headlights using an app and unlock doors.
But according to Miller and Valasek, the on-board Internet connection is a ‘super nice vulnerability’ for hackers.
All they have to do is work out the car’s IP address and know how to break into its systems and they can take control.
Independent security expert Graham Cluley said: ‘Note that the researchers believe that, although they’ve only tested it out on Jeeps, the attacks could be tweaked to work on any Chrysler car with a vulnerable Uconnect head unit.’
The incident is the latest hacking episode which shows just how vulnerable we are to modern technology.
It comes after the FBI claimed a US hacker took control of a passenger jet he was on in the first known such incident of its kind.
Chris Roberts is said to have plugged into the plane’s computer systems through the electronics box under his seat – and briefly moved the aircraft sideways.
Earlier this week it also emerged that hackers were threatening to release the confidential details of millions of people after stealing information from adultery website AshleyMadison.com.
After being contacted by the hackers nine months ago, Fiat Chrysler released an update to its car systems.
But users have to download it onto a memory stick and plug it into their USB port, or take it the vehicle to a local dealership.
In a statement to Wired.com Fiat Chrysler said: ‘Under no circumstances does FCA condone or believe it’s appropriate to disclose ‘how-to information’ that would potentially encourage, or help enable hackers to gain unauthorised and unlawful access to vehicle systems.
‘We appreciate the contributions of cybersecurity advocates to augment the industry’s understanding of potential vulnerabilities. However, we caution advocates that in the pursuit of improved public safety they not, in fact, compromise public safety.’