The DHSC said the vaccine would be 'made available across the UK from next week' and that the Joint Committee on Vaccination and Immunisation (JCVI) would publish final advice for the priority groups to receive the vaccine shortly.
Speaking to Sky News and the BBC this morning, Mr Hancock confirmed the UK would have 800,000 doses available to begin vaccination next week.
The news comes as NHS England published final details of the COVID-19 vaccination enhanced service (ES), under which GP practices will deliver the vaccine programme in primary care. Practices have been told that they need to sign up to the ES by 7 December.
GPs and their teams will be delivering the vaccine via designated sites that will operate across a PCN area or group of PCNs. Practices have been told they will be given 10 days notice of any delivery, meaning the earliest GPs could begin vaccination is around mid December.
NHS England also plans to provide vaccinations at hospital sites and mass vaccination centres and Mr Hancock suggested that hospital sites would be the first to deploy the vaccines.
The UK is the first country to approve the Pfizer/BioNTech vaccine. The government has 40m doses of the jab on order, with 10m expected to be available before the end of the year.
During a press briefing on Wednesday morning MHRA chief executive Dr June Raine said that the vaccine had been approved following an 'extremely thorough and scientifically rigorous review of all the evidence of safety, of effectiveness and of quality'. She added that 'no corners had been cut' in reviewing the evidence and that scientists and clinicians had been 'working around the clock' to review the data.
The MHRA has also agreed and reviewed the prescribing information for the vaccine so that 'healthcare professionals are very clear and can be very confident that the vaccine is being used in the correct way', Dr Raine said.
Professor Sir Munir Pirmohamed, chair of the Commission on Human Medicine's Expert Working Group, also revealed that no specific precautions were required on administering the vaccine in people who have previously had COVID-19 and testing for the virus would not be required before receiving the vaccine.
During the briefing, JCVI chair Professor Wei Shen Lim confirmed that the priority list for those receiving the vaccine would remain broadly in line with interim advice it issued ealier this year. This puts care home residents and staff in the first priority group, followed by those over 80 and healthcare staff.
He said that while care home residents were first on the list there would be some 'flexibility in terms of operational constraints'. He said: 'The JCVI's advice is that every effort should be made to supply vaccine and offer vaccines to care home residents. Whether or not that is actually doable is dependent on deployment and implementation.'
The Pfizer/BioNTech vaccine was shown to be 95% effective at preventing illness from COVID-19 in final results from its phase 3 trial, which also showed it to have a similar efficacy profile across all age ranges, including older people, and ethnic groups.
Those vaccinated with the jab require two doses, three weeks apart. However, using the vaccine poses a logistical challenge for the NHS. It needs to be kept at a temperature of -70 degrees Celsius and it only has an effective life of five days when moved to a fridge with a temperature between 2 and 8 degrees Celsius.
Latest guidance from Public Health England on the programme reveals that each pack of the jab that vaccination sites receive will contain 195 vials with 5 doses per vial.
The other vaccine likely to be used in the early stages of the vaccination programme is the Oxford/AstraZeneca vaccine, which has also been submitted to the MHRA for approval. The UK has 100m doses of the vaccine on order, with 4m likely to be available before the end of the year.
Interim phase 3 trial data showed that jab to be 70% effective overall, although a subset of the trial which received a half dose of vaccine first, followed by a standard second dose increased efficacy to 90%. A further trial plans to investigate this finding further.
A DHSC spokesperson said: 'The government has today accepted the recommendation from the independent MHRA to approve Pfizer/BioNTech’s COVID-19 vaccine for use. This follows months of rigorous clinical trials and a thorough analysis of the data by experts at the MHRA who have concluded that the vaccine has met its strict standards of safety, quality and effectiveness.
'The NHS has decades of experience in delivering large scale vaccination programmes and will begin putting their extensive preparations into action to provide care and support to all those eligible for vaccination.'