The UK has become the first country in the world to approve the Covid-19 vaccine from Pfizer and BioNTech, paving the way for vaccination to start next week.
The jab has been shown in studies to be 95% effective and works in all age groups.
The UK has ordered 40 million doses of the vaccine, enough to vaccinate 20 million people with two doses, given 21 days apart.
Around 10 million doses are expected to be available for use in the UK in the coming weeks for priority groups, including healthcare workers, with 800,000 doses arriving next week.
A list of who will receive the vaccine first will be set out later on Wednesday.
Prime Minister Boris Johnson said it is "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 told Sky News the UK was the first country in the world to have a "clinically authorised vaccine" and it would be deployed as "quickly as it is manufactured".
He added: "This is fantastic news.
"The MHRA, the fiercely independent regulator, has clinically authorised the vaccine for rollout.
"The NHS stands ready to make that happen.
"So, from early next week we will start the programme of vaccinating people against Covid-19 here in this country."
Mr Hancock said that losing his step-grandfather to Covid-19 has "made him more determined".
He said: "I have a big and complicated and loving family, and losing a member of your family is obviously a big thing for anybody.
"It's just made me more determined.
"This is a horrible disease and I've hated seeing so many people suffer from it.
"It just really brings it home when it's a member of your own family."
Mr Hancock said until vaccines were rolled out people needed to stick to the rules, saying: "We've got to get from here to there and we've got to keep people safe in the meantime."
There would be "three modes of delivery" of the vaccine, with hospitals, mass vaccination centres and GPs and pharmacists offering the jab to those most in need, he added.
"Fifty hospitals across the country are already set up and waiting to receive the vaccine as soon as it's approved, so that can now happen."
He said vaccinations will start with the most elderly, people in care homes and their carers, before coming down the age range, with NHS staff and the clinically extremely vulnerable also high on the priority list.
He told BBC Breakfast: "2020 has been just awful and 2021 is going to be better, and help is on its way with this vaccine.
"I'm confident now with the news today that from spring, from Easter onwards, things are going to be better and we're going to have a summer next year that everybody can enjoy."
On the challenge posed by the need for the vaccine to be stored at an ultra-low temperature of around minus 70C, he added: "This is a challenging rollout and the NHS in all parts of the UK stands ready to make that happen.
"They are used to handling vaccines and medicines like this, with these sorts of conditions.
"It's not easy but we've got those plans in place."
England's chief medical officer, Professor Chris Whitty, said the vaccine approval is "excellent news and a step towards normality".
He tweeted: "It will take until spring until the vulnerable population who wish to are fully vaccinated. We can't lower our guard yet."
Nadhim Zahawi, the newly-appointed minister responsible for overseeing the vaccination rollout, tweeted: "Major step forward in the fight against Covid-19 today."
The UK was the first country to sign a deal with Pfizer/BioNTech – now we will be the first to deploy their vaccine
To everyone involved in this breakthrough: thank you
In years to come, we will remember this moment as the day the UK led humanity's charge against this disease
— Alok Sharma (@AlokSharma_RDG) December 2, 2020
Information obtained by the PA news agency on the jab's rollout says once the vaccine arrives in the UK from Pfizer's plant in Belgium, batches will be checked at a central depot to ensure their quality.
The vaccine will then be unloaded and moved to storage freezers where it will undergo an additional temperature check.
Public Health England (PHE) will process orders placed by the NHS for next day delivery to hospital hubs around the UK.
Defrosting the vaccine for use takes several hours and then extra time is needed to prepare the vaccine for administering as doses.
Business Secretary Alok Sharma tweeted: "The UK was the first country to sign a deal with Pfizer/BioNTech, now we will be the first to deploy their vaccine.
"To everyone involved in this breakthrough: thank you.
"In years to come, we will remember this moment as the day the UK led humanity's charge against this disease."
Scotland's First Minister Nicola Sturgeon said it was "the best news in a long time".
She tweeted: "@scotgov ready to start vaccinations as soon as supplies arrive."
Sir Simon Stevens, chief executive of the NHS in England, said the vaccination programme would be the "largest-scale vaccination campaign in our country's history".
In a statement, he said: "This is an important next step in our response to the coronavirus pandemic and hospitals will shortly kick off the first phase of the largest-scale vaccination campaign in our country's history.
"The NHS has a proven track record of delivering large-scale vaccinations from the winter flu jab to BCG and, once the final hurdles are cleared and the vaccine arrives in England's hospitals, health service staff will begin offering people this ground-breaking jab in a programme that will expand to cover the whole country in the coming months."