The new 5 pounds (USD 8.2, 6.0 euro) note made of polymer will be issued in 2016 and feature World War II prime minister Winston Churchill, Britain's central bank said.
A polymer 10 pounds note featuring novelist Jane Austen will follow around a year later.
More than 25 other countries have flexible polymer banknotes, with at least seven using only plastic notes.
Sterling is the first of the world's major currencies -- ahead of the US dollar, the euro, the Japanese yen and the Swiss franc -- to switch to polymer.
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Though slightly smaller, the new notes will retain a similar layout, featuring a 1990 portrait of Queen Elizabeth II, and a historical figure on the reverse.
The BoE first began issuing handwritten notes shortly after it was established in 1694. The first fully-printed notes appeared in 1853.
The United Kingdom's first polymer banknote was a commemorative 5 pounds note to mark the year 2000, issued by Northern Ireland's Northern Bank.