Number one will be assigned First Class passengers on long-haul flights and short-haul travellers on BA's business class, Club Europe, as well as Gold members of the BA Executive Club
Next will be business class Club World passengers on long-haul flights, and Silver members of the Executive Club.
Group three will be passengers in World Traveller Plus, which is BA's premium economy, as well as Bronze members.
Normal economy passengers will be in group four.
The indignity of boarding the plane last will be given to those travelling on the cheapest, hand-baggage only fares. These fares were introduced in 2013 as BA sought to compete with easyJet.
Passengers with mobility issues or who are travelling with young children will still be able to board ahead of everyone else.
The change is revealed in an internal document, which says: "This method has been used all around the world by many airlines and aligns BA with partners American Airlines and Iberia.
"Group boarding simplifies the process, making it easier for customers to understand the boarding sequence at the gate."
Passengers reacted with anger and bemusement on social media, and accused BA of "losing the plot".
Some described the prospect of being in group five as having to do "the walk of shame".
Earlier this year it emerged that BA is on the verge of having its rating cut from four to three stars, or of five, by research firm Skytrax.
This would put Britain's flagship carrier on a par with Ryanair and Uzbekistan Airways, and comes after a string of controversies over baggage charges and the removal of perks for first-class passengers and the withdrawal of free food on European economy services.
A spokesman for British Airways confirmed the move, saying: "We are always looking at ways to improve the airport experience for our customers.
"Earlier this year we were the first UK airline to introduce automated biometric technology, with the launch of self-service boarding gates, and we also installed self-service bag drop points at Heathrow and Gatwick giving our customers an even quicker check-in experience.
"Next month we are looking at introducing new boarding procedures to further improve the customer journey by creating a number of groups to speed up the process.
"This method has been used by airlines around the world for a number of years, including by our partners American Airlines, Iberia and Qatar."