The UK Medicines and Healthcare products Regulatory Agency (MHRA) said that approval was granted after a rigorous and detailed scientific review.
People aged 18 or over will receive two shots of the vaccine with the second dose administered 4-12 weeks after the first.
Britain has already started to administer a vaccine developed by Pfizer/BioNTech, but the Astra/Oxford option has advantages in terms of storage, ease of manufacture and cost.
The Astra/Oxford vaccine, for example, can be stored at normal fridge temperatures of between 2C to 8C making it far easier to distribute than the Pfizer/BioNTech jab that needs temperatures of minus 70c.
Those people deemed most at risk from COVID-19 will be the first to receive the vaccine, said the government, which described the approval as a triumph for British science.
"We will now move to vaccinate as many people as quickly as possible," said Prime Minister Boris Johnson, with the UK already having ordered 100mln doses.
Scientists believe that with both the Astra/Oxford and Pfizer/BioNTech vaccines there will be capacity for 2mln jabs per week.
Britain is facing a surge of new COVID-19 infections, many of which are from a new strain of the virus that was only recently identified.
Swathes of the country are shortly expected to follow London and south-east and be placed in the strictest level of Tier-4 restrictions due to the rising number of new cases.
More than 53,000 cases of COVID-19 were recorded in the UK yesterday, the highest number recorded since mass testing began, with a further 414 deaths of people who tested positive for the virus.
The total number of people in the UK officially who have died from the virus has now topped 71,000 but the number is believed to be substantially higher including cases where the virus has not been attributed as the cause.
Though now approved in the UK, getting the jab elsewhere might still be some time away.
Oxford University and AstraZeneca developed the new vaccine in only ten months and there has been a concern in Europe and the US about the speed of progress.
The European Medicines Authority (EMA) deputy executive director was quoted yesterday as saying that an application for approval in Europe had yet to be filed.
“We need additional data about the quality of the vaccine. And after that, the company has to formally apply.” Noel Wathion told Belgian newspaper Het Nieuwsblad.
US regulators have also been taking a cautious approach to the vaccine, especially after it was revealed that a half-dose was more effective in trials than two full shots.
Approval was granted by the MHRA for two full shots rather than half-doses.
Shares in AstraZeneca rose 0.3% to 7,483p.