The jab has been shown in studies to be 95% effective and works in all age groups.
The Joint Committee on Vaccination and Immunisation (JCVI), which advises ministers, said vaccines should first be offered to elderly people in care homes and care home workers.
Next on the priority list are those aged 80 and above and frontline health workers.
All those aged 75 and over should be vaccinated next, followed by those 70 and over and clinically “extremely vulnerable” individuals, it said.
People aged 65 and over are next in line, alongside anyone aged 16 to 64 who has underlying health conditions which put them at a “higher risk of serious disease and mortality”.
Those aged 60 and over will be vaccinated next, followed by those aged 55 and over, and then those aged 50 and over.
No decisions have yet been made on priorities for under-50s.
The UK has ordered 40 million doses of the Pfizer vaccine, enough to vaccinate 20 million people with two doses, given 21 days apart.
Health Secretary Matt Hancock said 800,000 doses of the jab will arrive next week.
He said millions more doses were due in the coming weeks.
Studies on the vaccine show it has to be stored at minus 70C but is also stable at 2C to 8C for a short time, meaning it could possibly be sent to different locations.
But it is thought operational reasons may prevent care home residents getting the jab first.
Care England, a leading care provider membership group, said it had received no clear communications from the Government.
It believes it is unlikely the Pfizer/BioNTech vaccine, approved today by the Medicines and Healthcare products Regulatory Agency (MHRA), will be available in care homes next week.
Professor Martin Green, Care England chief executive, said: “I think it will be difficult for the Pfizer/BioNTech vaccine to be used in care homes because of the difficulty of storage and the low temperatures required.
“In light of this, we need the Oxford vaccine to be approved as soon as possible and a vaccination programme put in place so that care home residents can be protected from Covid-19.”
The Department of Health has been contacted for comment.
Prime Minister Boris Johnson said the announcement was “fantastic” news, tweeting: “It’s the protection of vaccines that will ultimately allow us to reclaim our lives and get the economy moving again.”
A Department of Health and Social Care spokesman said the Medicines and Healthcare products Regulatory Agency (MHRA) had approved the jab after “months of rigorous clinical trials and a thorough analysis of the data by experts” from the regulator.
He said they have concluded that the vaccine has “met its strict standards of safety, quality and effectiveness”.
Health secretary Matt Hancock confirmed vaccinations will start with the most elderly, people in care homes and their carers, with NHS staff and the clinically extremely vulnerable also high on the list.
Dr June Raine, head of the regulator which approved the Pfizer and BioNTech vaccine, said “no corners have been cut” in assessing its safety.