Sajid Javid said the top-up jab will help those at the highest risk of serious illness maintain a high level of protection against the virus.
The NHS in England will offer people the jab from around six months after their last dose, with further details due to be set out shortly.
In interim guidance published for planning purposes, the JCVI said a further dose for older people and those at risk is likely to be needed this autumn.
This is because, although vaccines offer strong protection, their effectiveness does wane over time and Covid surges are expected in winter.
The autumn jab campaign is expected to cover a wider group of people than in the spring and could include any new Covid vaccines that are available.
It has not yet been decided whether all those currently eligible for an annual flu vaccination will be included.
Mr Javid said: “Thanks to our Covid-19 vaccination rollout, we are already the freest country in Europe.
“It has saved countless lives, reduced pressure on the NHS and is allowing us to learn to live with the virus.
“Today I have accepted the advice from the independent Joint Committee on Vaccination and Immunisation (JCVI) to offer, from spring, an additional Covid-19 booster jab to people aged 75 years and over, residents in care homes for older adults, and people aged 12 years and over who are immunosuppressed.
“All four parts of the UK intend to follow the JCVI’s advice.
“We know immunity to Covid-19 begins to wane over time.
“That’s why we’re offering a spring booster to those people at higher risk of serious Covid-19 to make sure they maintain a high level of protection. It’s important that everyone gets their top-up jabs as soon as they’re eligible.
“The JCVI will keep under review whether the booster programme should be extended to further at-risk groups.”