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

Stuart Brownhill, 59, was absent during a roll-call at 05:00 BST at the North Sea Camp prison, near Boston, police said.
He murdered Lynne Taylor while her 11-year-old son slept in their home in Werneth, Oldham, in 1984 and was jailed for life at Manchester Crown Court the following year.
Police have asked the public not to approach him.
More on this story and others news in Lincolnshire
Brownhill met Ms Taylor on a night out and later set fire to her home. He admitted he strangled Ms Taylor after trying to rape her and that he knew the boy was asleep in the property when he started the fire.
He is described as 5ft 8in tall, bald, and has a green right eye and a blue left eye. Officers believe he may be wearing a brown jacket and black boots.
The force have appealed for anyone who sees him to contact them immediately by dialling 999.
Officers said anyone with information on his whereabouts should call 101.

Members of the RMT union will walk out for 48 hours from Sunday 7 August, 24 hours on Thursday August 11 and over the weekend of 13/14 August.
The RMT is against the increased use of trains on which the driver opens and closes the doors at stations.
ScotRail has said such operations are already common on the network.
RMT general secretary Mick Cash said: "Recent rock-solid strikes on ScotRail have been supported by the travelling public who understand that the staff are fighting for the basic principles of rail safety.
"In spite of this, Abellio/Scotrail continue to ignore the strength of feeling amongst their staff and passengers over the extension of driver-only operation."
ScotRail says 59% of customers already travel on a train where the doors are safely opened and closed by the driver, and insists that the job, pay and conditions of conductors are guaranteed.
Phil Verster, managing director of Scotrail Alliance, has previously said: "This industrial action by the RMT is not about safety, it's not about a second person on a train and it's not about jobs or pay and conditions.
"It is about modernisation of the railway and preparing us for a railway that Scotland can be proud of for the next 40 or 50 years."
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.
[NEXT_CONCEPT]
A convicted murderer has absconded from an open prison in Lincolnshire.
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Workers on ScotRail are to stage a fresh wave of strikes in a long-running dispute over the increased use of trains without guards.