Officials said the vaccine will be made available in the UK 'from next week'.
Jersey will get its vaccine supply through the UK.
A UK Department of Health and Social Care spokesman said: 'The government has today accepted the recommendation from the independent Medicines and Healthcare products Regulatory Agency (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 Joint Committee on Vaccination and Immunisation (JCVI) will shortly also publish its latest advice for the priority groups to receive the vaccine, including care home residents, health and care staff, the elderly and the clinically extremely vulnerable.
'The vaccine will be made available across the UK from next week.'
Fort Regent will be used as a mass vaccination centre.
The first people to receive the vaccine will be the approximately 1,000 residents of nursing and residential homes. A team of vaccinators will visit all care homes to offer the vaccination to all residents.
The next people to be vaccinated will be care home and home care staff. They will be vaccinated at the Queen’s Hall in Fort Regent.
The next group will be Islanders aged 80+ followed by nearly 5,000 front line Health and Community Services staff, and then other Health and Community Services staff, GPs and pharmacists.
Next will be Islanders aged 75-79, 70-74 and 3,000 high risk Islanders, followed by 65-79-year olds. Younger people aged 50-64 will be next, followed by the remainder of the population. All these groups will be vaccinated at Fort Regent.