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.
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.
Mr Carney said: "Our polymer notes will combine the best of progress and tradition.
"They will be more secure from counterfeiting and more resistant to damage, while celebrating the history and tradition that is important both to the Bank and the nation as a whole.
"By consulting widely on the switch to polymer, and by putting in place a new process for selecting banknote characters with much more public input, we have reinforced the commitment to openness and transparency which lies at the heart of the Bank of England's commitment to accountability.
"Together, these announcements ensure that our banknotes will remain both a national symbol and a source of national pride."
Mr Carney brushed off fears that the notes would be damaged by heat, saying: "They don't melt in the heat, unless it's extreme heat. You have to get above boiling for it to actually happen.
The Bank's new guidelines on selecting historical characters for notes come after an outcry over the lack of women on paper money.
It followed the decision to replace prison reformer Elizabeth Fry with Sir Winston Churchill on the £5 note, meaning there would be no notes featuring the face of a woman - other than the Queen.
Bank officials agreed to meet leading campaigner Caroline Criado-Perez after thousands signed a petition in protest. Later, novelist Jane Austen was named as the face of the new £10 note.
Mr Carney has also come under pressure over the lack of women on the rate-setting monetary policy committee - recently assuring MPs that addressing such issues would be "central to our priorities in the coming years".
Guidelines set out today detail a set of principles for character selection as well as a new process drawing more heavily on input from the public and independent experts which "ensures that decision-makers consider the equality implications of choices".
The Bank will also seek to celebrate individuals who have "shaped British thought, innovation, leadership, values and society" while seeking to avoid those "who would be unduly divisive".
It will not represent living characters on notes, other than the monarch.