The deal with GlaxoSmithKline will enable the vaccine to be rolled out "this year", easing one of the "biggest worries" for parents, he said.
It follows a long-running stand-off over its cost.
Advisers recommended last year that all UK children over two months old should be given the vaccine on the NHS.
Campaigners have warned the Department of Health that delays are putting children's lives at risk.
Scotland's health secretary, Shona Robison, said the vaccine would be introduced to the immunisation programme for all infants in Scotland "as quickly as possible" following the deal - which was also made on behalf of the devolved government.
Mr Hunt said he was "delighted" to have secured an agreement with GSK - the company that now manufactures the vaccine.
It follows lengthy negotiations with another supplier - Novartis - which used to own the vaccine, called Bexsero.
GSK acquired the vaccine from Novartis, which resulted in the price of the vaccine being reduced and the deal being struck, Mr Hunt said.
Announcing the agreement, he said: "I think that this is something families across the country - particularly ones with young children - will particularly welcome."
The vaccine has been available privately in the UK - but the deal could mean the jab is offered as part of a routine childhood vaccination programme.
It comes after charities called for urgent action from the prime minister and Mr Hunt to conclude negotiations with manufacturers.
Meningitis is a bacterial infection that usually affects children under the age of one. There are about 1,870 cases of meningitis B each year in the UK.
Symptoms include a high fever with cold hands and feet, confusion, vomiting and headaches. Most children will make a full recovery with early diagnosis and antibiotic treatment.
It is fatal in one in 10 cases. About one in four of those who survive is left with long-term problems, such as amputation, deafness, epilepsy and learning difficulties.
Q&A: Meningitis B vaccine
An agreement has been reached with the drug manufacturer GSK to provide a meningitis B vaccine for all UK babies, Health Secretary Jeremy Hunt has said.