"This work, which used a tentative unification of Einstein's theory of general relativity with quantum mechanics, reported that black holes should not be completely black, instead emitting radiation, meaning they evaporate and eventually disappear", Royal Mint said in a statement.
A limited number of gold and silver presentation coins, celebrating the life of Stephen Hawking, featured on the Royal Mint website and costing from £55 to £795, have all been reserved and are no longer available for purchase.
One side of the coin features an image of a black hole with the scientist's name inscribed above it, while the reverse is an image of Queen Elizabeth II.
He once told the BBC he thought his discovery that black holes were not entirely black would be his "greatest achievement".
Ellis said she wanted to reflect the way Hawking made hard subjects accessible, engaging and relatable.
"Hawking, at his playful best, invites the audience to contemplate peering into a black hole before diving in".
Known as the Bekenstein-Hawking formula - an honour shared with the theoretical physicist Jacob Bekenstein - its derivation was a significant step forward in efforts to make the weird properties of black holes fit with existing laws on energy.
The physicist died a year ago at the age of 76, having become one of the most renowned leaders in his field.
With this coin, Stephen Hawking becomes one of an elite group of scientists to have been honoured on United Kingdom coins, alongside the likes of Charles Darwin in 2009 and Sir Isaac Newton in 2017.
Hawking, who died on March 14 previous year, had once said that he thought his discovery that black holes were not entirely black would be his "greatest achievement".