Flights will get under way on Friday (24 April) and will run every second day, with departures alternating between Auckland and Christchurch.
Lord Goldsmith, the minister responsible for New Zealand, said vulnerable Britons and those "most at risk from coronavirus" would be prioritised.
According to the FCO, some 2,600 Britons have made their way home from New Zealand via commercial means since the Covid-19 outbreak began.
However, the government announced on Monday (20 April) it was stepping in to provide a charter programme now it was "no longer possible" to book commercial flights back to the UK from New Zealand.
"We promised we would do everything we could to help get Britons home," said Goldsmith. "Getting a commercial flight from New Zealand is now extremely difficult, so we are now going to bring back vulnerable British travellers on charter flights and will continue to support those who remain in the country."
Laura Clarke, British High Commissioner to New Zealand, added: "We are doing all we can to help British people get back home to the UK, and new charter flights will help more people – particularly the most vulnerable – to do that.
"My team and I will continue to do all we can to support those who are still in New Zealand, throughout this crisis and beyond."
The FCO is classifying those over the age of 70, those under 70 with underlying or complex health conditions, or those who are pregnant as vulnerable for the purposes of the rescue flights.
Eligible travellers will be contacted by the High Commission to book their flights; those ineligible will continue to be able to access support from High Commission staff in New Zealand.
Tickets will cost £800; those who cannot afford this, and have exhausted other means to get home, "may be eligible to apply for an emergency loan from public funds".
