The polymer fiver is said by the Bank of England to be cleaner, safer and stronger than paper notes, lasting around five years longer.
The first print-run of 440 million new fivers marks the start of the old notes' withdrawal as they are banked by retailers and businesses.
While some people may start to see the new fiver immediately at cash machines and bank counters, for others it may take a few weeks.
The Bank has been working with the cash industry to help get machines ready for the new £5 notes. It said not all machines will be ready from day one and it will continue to work with businesses to ensure a smooth transition.
The old fiver, featuring prison reformer Elizabeth Fry, can still be used in shops until it ceases to become legal tender after May 5 2017.
The new £5 note paves the way for a new generation of security features, making it harder to counterfeit. They include a see-through window featuring the Queen's portrait as well as Big Ben shown in gold foil on the front of the note and silver on the back.
Bank of England Governor Mark Carney said: "The new fiver commemorates one of the greatest statesmen of all time, Winston Churchill, who remarked that 'a nation that forgets its past has no future'.
"Banknotes are repositories of the United Kingdom's collective memory, and we will be reminded of Churchill's enormous contributions as he once again becomes part of our daily lives as the new fiver flows out into tills and pockets."
Carney said of the new note: "The use of polymer means it can better withstand being repeatedly folded into wallets or scrunched up inside pockets and can also survive a spin in the washing machine.
"We expect polymer notes to last at least two and-a-half times longer than the current generation of fivers and therefore reduce future costs of production."
While the new fiver is the first Bank of England note to be printed on polymer, some parts of the UK have already experienced plastic banknotes.
In March 2015 in Scotland, Clydesdale Bank issued two million £5 polymer banknotes to commemorate the 125th anniversary of the opening of the Forth Bridge.
The announcement by the Bank of England in 2013 that Fry would be replaced with the former prime minister caused an outcry as it could have meant that, apart from the Queen, there would be no female faces on the UK's notes.
Thousands signed a petition in protest. It was subsequently announced that novelist Jane Austen would be the face of the new £10 note from summer 2017.
Like the new fiver, the new £10 and £20 notes will also be printed on polymer.
The Bank previously announced artist JMW Turner will appear on the next £20 banknote, due to be issued by 2020.
To help blind and vision impaired people distinguish between denominations, the new notes will retain tiered sizing and include bold numerals and similar colour palettes to existing notes.
The new polymer £10 and £20 notes will also have tactile features created by a series of raised dots. The £5 note will be distinguishable by the absence of this feature.
Born at Blenheim Palace on November 30 1874, Sir Winston Leonard Spencer Churchill was elected as a Conservative MP for Oldham in 1900. In May 1940 he became prime minister, replacing Neville Chamberlain and leading the newly-formed national government.
In his first speech to the new administration, he declared: "I have nothing to offer but blood, toil, tears and sweat", - words which are depicted on the new £5 note.
Sir Winston's strong leadership qualities during the Second World War earned him a vast international following, particularly in the United States where he was granted honorary US citizenship. He has been portrayed on the postage stamps of 150 nations.
During his lifetime, Sir Winston received 37 orders, decorations and medals including Companion of Honour, Order of Merit, Order of the Garter and in 1953 the Nobel Prize for literature.
He died at the age of 90, on January 24 1965, and was given a state funeral. Sir Winston was also the first commoner to be portrayed on a British coin - the 1965 crown or five shilling piece.