The sculpture is on a plinth in Waterloo Place, just off The Mall, and bears Banksy's signature.
It is positioned on a traffic island in Pall Mall where Banksy said: "There was a bit of a gap."
In a humorous video posted on Thursday on his Instagram account, Banksy showed snippets of how the sculpture was put up overnight.
Before the artist's post, locals and tourists gathered to inspect the statue on the assumption it was Banksy's work because his signature was scrawled at the base of the plinth.
The statue is situated close to those of King Edward VII, who reigned between 1901 and 1910, and legendary nurse Florence Nightingale as well as the Crimean War Memorial.
The Press Association understands the artist revealed the unsolicited monument at some point in the early hours of Wednesday, claiming it a day later.
Banksy, whose real name has never been officially confirmed, has become famous across the world for politically-charged murals including 2002's Girl With Balloon, 2003's Love Is In The Air and 2004's Kissing Coppers.
Banksy claimed an artwork of two figures that appeared on the side of a building in Bayswater, London, in December.
In September, Banksy made headlines with a mural depicting a protester lying on the ground, holding a blood-spattered placard, while a judge, in a wig and gown, looms over him, wielding a gavel.
The painting appeared on an external wall of the Queen's Building, in the Royal Courts of Justice complex, however it was swiftly covered up and guarded by security staff, before work began to remove it.
The art was interpreted by some as a comment on the arrest of hundreds of people for supporting Palestine Action by holding up placards at protests.
with AP
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