A catch-up campaign has been planned for slightly older children so they did not miss out, it added.
Until now, parents who wanted to protect their child against the chickenpox varicella virus have usually had to pay up to £200 privately.
“Being able to provide protection for children against chickenpox for the first time on the NHS is truly a historic moment,” said Dr Trevor Smith, from NHS England South West.
“This will help us keep our children healthier, enabling them to stay in school and supporting the wider NHS goal of moving from sickness to prevention.”
The latest data, external shows half of children will contract chickenpox by the age of four, and 90% by the age of 10.
They are often told to stay off school until all spots have formed a scab, which is usually five days after the spots first appear.
The NHS said the new vaccine would mean children miss fewer days in nursery or school, and reduce time parents need to take off work to care for them.
It added that local GP surgeries would begin contacting families to help them book appointments to receive the jab.