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The Men B vaccine will be given to babies at two months, four months and 12 months old in a move which meningitis charities say will "save lives straight away".
It will be the first national and publicly-funded programme against the deadly infection in the world and from August, another meningitis vaccine - Men ACWY - will be offered to 17 and 18-year-olds and students starting university this year.
In announcing the vaccine, the Minister said: "I am very proud that we will be able to offer families extra peace of mind with these new vaccination programmes from this summer.
"The nationwide meningitis B programme will mean that England and Scotland lead the world in offering children protection from this devastating disease. These two new vaccination programmes will offer families extra peace of mind."
Negotiations over the cost of the new baby vaccine were finally resolved in March, meaning the Men B programme will be rolled out in England and Scotland from 1 September, with Wales and Northern Ireland expected to follow suit shortly afterwards.
The vaccine will be offered alongside other routine infant vaccines through the NHS childhood immunisation programme, the Department of Health and Scottish Government said.
Tests suggest that the new Men B vaccine, called Bexsero, will protect against around 90% of the meningococcal group-B bacteria strains circulating in the UK.
Meningitis B is a bacterial infection that particularly affects babies under the age of one and is also common in children under five.
The disease infects the protective membranes surrounding the brain and spinal cord. If the infection is left untreated, Men B can cause severe brain damage and blood poisoning - and in some cases, it can kill.
About 1,200 people - mainly babies and children - get meningitis B each year in the UK, with around one in 10 dying from the infection, according to NHS figures.
Meningitis Now chief executive Sue Davie added: "We're delighted that this milestone in the journey to introduce these vaccines and protect our babies and young people from the devastation meningitis causes has been reached.
"These measures will start to save lives straight away and for years to come. But it's vital to learn the signs and symptoms, stay vigilant and seek immediate medical help if you suspect the disease."