The 12-sided coins, which resemble the old threepenny bit, will be in use from Tuesday, March 28.
They are being made at the Royal Mint in Llantrisant, South Wales, at a rate of three million per day. The coins have high-tech security features, including a hologram.
It might take a little while for people to start seeing the new £1 coins in their change as they gradually filter into general use.
The old “round pound”, which was introduced more than 30 years ago, will be in circulation alongside the new coin until it ceases to be legal tender on October 15.
£1 coins were first launched on April 21, 1983, to replace £1 notes. The Royal Mint has produced more than two billion round pound coins since that time.
The production of the new coins follows concerns about round pounds being vulnerable to sophisticated counterfeiters.
Around one in every 30 £1 coins in people’s change in recent years has been fake. The new coin has a gold-coloured outer ring and a silver-coloured inner ring.
It is based on the design of the old 12-sided threepenny bit, which went out of circulation in 1971.
People have been urged to return the old round pounds before they lose their legal tender status. They can either spend them, or bank them.
More than 70 million £1 coins are thought to be stashed away in piggy banks, purses and jars.
Some of the round £1 coins returned by the public will be melted down and reused to make the new £1 coin.