Plastic bank notes are to be issued by the Bank of England for the first time when the new £5 featuring Sir Winston Churchill appears in 2016.
A £10 note featuring Jane Austen to follow around a year later will also be made from polymer rather than the cotton paper currently used, the Bank said.
It follows a three-year research programme that concluded plastic notes stay cleaner for longer, are more difficult to counterfeit and are at least 2.5 times longer-lasting.
A public consultation including events at shopping centres across the UK, giving people the chance to handle the notes, found 87% of 13,000 individuals who responded were in favour of polymer.
Bank governor Mark Carney said: "Ensuring trust and confidence in money is at the heart of what central banks do. Polymer notes are the next step in the evolution of bank note design to meet that objective.
"The quality of polymer notes is higher, they are more secure from counterfeiting, and they can be produced at a lower cost to the taxpayer and the environment."
The new notes will retain their familiar look, the Bank said, including the portrait of the Queen and a historical character.
Meanwhile, the Bank announced new guidelines on how it chooses historical figures to feature on bank notes, which include the aim that they should "reflect the diverse nature of British society".
It will be the first time plastic notes have been used in the Bank's 300-year history.
A contract is expected to be signed with Innovia Security to supply polymer material, which would see Innovia establish a polymer production plant in Wigton, Cumbria.
The Bank acknowledged when it launched its consultation in September that plastic banknotes were more expensive to produce but argued that because they are longer-lasting they should prove cheaper in the long run.
It also says that, being thin and flexible, they can fit into wallets as easily as paper banknotes.
But the Bank said it would only proceed with plastic notes if persuaded that the public would have confidence in, and be comfortable with, them.
It said feedback from its consultation showed people who had been able to see and handle the notes were 20% more likely to support polymer than those who responded on the internet.
The Bank said it was continuing dialogue with the cash-handling industry over the changes that would be needed to ensure a smooth introduction of the first plastic note.
It said the new notes would be slightly smaller than existing paper equivalents, but the practice of note size increasing with denomination will be maintained.
The Bank said present currency was larger and more unwieldy for cash handling technology and everyday use, and smaller notes would reduce printing and storage costs.
The contract for printing Bank of England notes from April 2015 is currently being tendered. They will continue to be printed at the Bank's printing works in Debden, Essex.
The polymer £5 will measure 125mm (4.9 inches) by 65mm (2.5 inches), and subsequent denomination sizes will be fixed at 7mm (0.27in) longer and 4mm (0.15in) higher, making the £10 note slightly larger than the equivalent euro notes.
More than 25 countries issue polymer banknotes, including Australia - which began printing them in 1988 - as well as New Zealand, Mexico, Singapore, Canada, and most recently Fiji and Mauritius.
The Bank first began issuing handwritten notes shortly after it was established in 1694. The first fully-printed notes appeared in 1853.
Last year there were 2.9 billion notes in circulation, with a face value exceeding £52 billion, according to the Bank's figures.