The £20 note featuring composer Sir Edward Elgar is to be withdrawn from circulation by the Bank of England from the end of June.
Most banks, building societies and Post Offices will accept the Elgar notes for deposits and other transactions for "several months" beyond June.
But it will be at their discretion whether they exchange the notes.
The Elgar £20 banknote, first issued in June 1999, has gradually been replaced by the Adam Smith £20 note since 2007.
"We said at the time that the two designs would circulate in tandem, with the Elgar notes gradually being withdrawn over the next few years," said the Bank of England's chief cashier, Andrew Bailey.
"It is time now to withdraw the Elgar £20 notes completely, with the Adam Smith £20 banknotes to be the only £20 note design continuing in circulation."
There are approximately 1.5 billion £20 notes in circulation, of which an estimated 150 million are Elgar notes.
The Bank of England said it would always exchange its old notes.