The round £1 will be legal tender alongside the new, more-secure coin until 15 October.
The public are being urged to use their current £1 coins or bank them before they lose their legal tender status.
The government estimates around a third of the £1.3 billion worth of coins stored in piggy banks or saving jars around the UK are the current £1 style.
Some of those returned by the public will be melted down and used to make the 12-sided version.
The new style was announced in the 2014 budget and has been billed by the Royal Mint as "the most secure coin in the world".
Its introduction will come as a new set of coin designs are also brought into circulation, celebrating the achievements of Jane Austen and Sir Isaac Newton.
The Royal Mint said the new designs have a "strong pioneering theme" and will start appearing this spring.
A Jane Austen £2 coin will celebrate the author 200 years after her death, while another £2 version will remember the Royal Flying Corps.
A 50p coin will mark the achievements of mathematician Sir Isaac Newton, a one-time Master of the Royal Mint.
Dr Kevin Clancy, director of the Royal Mint Museum, said: "This is a particularly significant year in Royal Mint history as we welcome in the new 12-sided £1 coin, with its innovative security features.
"This year we also mark the achievements of Jane Austen, Sir Isaac Newton and the Royal Flying Corps - all pioneers in their own field."
The new 12-sided £1 coin will enter circulation on 28 March, the government has said.