Guided by a system of sensors and cameras, the cars will, for the first time, be driven on public roads in a series of trials that will last between 18 and 36 months.
UK cities can now bid for a share of a £10 million competition to host the trials, with up to three cities being selected.
But motoring groups have warned that road users will be wary of the introduction of driverless vehicles.
Ministers have also launched a review to look at current road regulations to establish how the UK can remain at the forefront of driverless car technology and ensure there is an appropriate regime for testing driverless cars in the UK.
Two areas of driverless technology will be covered in the review: cars with a qualified driver who can take over control of the driverless car and fully autonomous vehicles where there is no driver.
The go-ahead for the new cars was given by Business Secretary Vince Cable who, with Science Minister Greg Clark, tested a driverless car at the headquarters of motor industry research organisation MIRA at Nuneaton in the West Midlands.
Mr Cable said: "The excellence of our scientists and engineers has established the UK as pioneers in the development of driverless vehicles through pilot projects.
"Today's announcement will see driverless cars take to our streets in less than six months, putting us at the forefront of this transformational technology and opening up new opportunities for our economy and society.
"Through the Government's industrial strategy we are backing the automotive sector as it goes from strength to strength. We are providing the right environment to give businesses the confidence to invest and create high skilled jobs."
Transport Minister Claire Perry said: "Driverless cars have huge potential to transform the UK's transport network. They could improve safety, reduce congestion and lower emissions, particularly CO2.
"We are determined to ensure driverless cars can fulfil this potential which is why we are actively reviewing regulatory obstacles to create the right framework for trialling these vehicles on British roads."
Mr Clark said: "Britain is brilliantly placed to lead the world in driverless technology"
Driverless cars are already in use in a number of countries, including America, Japan and Sweden.
But AA president Edmund King said that a recent AA/Populus survey of more than 23,000 AA members showed that 43% did not agree that UK legislation should be amended to even allow trials of the technology.
And the RAC said: "We suspect it will be difficult for people to come to terms with giving up control of their vehicle to a computer."
Mr King said: "Today's announcement takes us closer to seeing fully autonomous vehicles on our roads but it will take some time for them to become commonplace.
"Many drivers are still resistant to change as 65% enjoy driving too much to ever want the vehicle to take over from them."
RAC technical director David Bizley said: "Many vehicles already have features such as automatic braking and it is claimed that driverless technology is able to identify hazards more effectively than a person can.
"But many motorists will be concerned about not being able to control the speed of their vehicle for the conditions or layout of the road in front of them."
AA Insurance director Simon Douglas said: "Driverless cars will need a fresh approach to insurance. Motor insurance is based on risk and much of the cost of a policy is associated with the driver - such as age, experience, past claims and convictions.
"If that element is largely removed then driverless cars could potentially attract significantly lower premiums than conventional vehicles, providing the technology that operates them is reliable and demonstrably reduces the likelihood of a collision."
James Dalton, head of motor insurance at the Association of British Insurers, said: "The insurance industry is working with Government, vehicle manufacturers, regulators, the legal community and through the industry's research and repair centre on this potentially life-changing and life-saving technology.
"Although further research needs to be carried out, with human error accounting for around 90% of road accidents, the potential safety implications of autonomous technology are significant."
Campaign for Better Transport chief executive Stephen Joseph said: "Government support for trials of this technology is welcome, but caution is needed. The UK's busy roads and cities would suffer if the new cars increase traffic and car dependency.
"We want the Government to broaden its approach and look at how these technologies can be best used across the transport sector, so as to improve safety, manage freight better and improve rail services."
He went on: "Autonomous cars won't remove the need to invest in making walking and cycling safer and more attractive, which we know is essential not only in helping people become more active but in addressing pollution."
Road Safety Markings Association national director George Lee said: "By 2025, at least half the travel on Europe's roads will be in vehicles that can read the road ahead, including markings and signs.
"But vehicles, like drivers, cannot function if basic road markings and signs are non-existent, non-compliant, worn out, obscured, inconsistent or confusing."