One of the artworks shows a scarecrow figure, similar to Basquiat's 1982 piece "Boy and Dog in a Johnnypump", being searched by two police officers.
A picture of the mural appears on Banksy's Instagram feed with the caption: "Portrait of Basquiat being welcomed by the Metropolitan Police -- an (unofficial) contribution with the new Basquiat show".
The second shows people queueing up to ride a Ferris wheel with crown-shaped gondolas.
The murals appeared over the weekend near the Barbican Centre, which will open its exhibition on the American graffiti artist on Thursday.
Banksy said on Instagram: "Major new Basquiat show opens at the Barbican -- a place that is normally very keen to clean any graffiti from its walls."
The event is being billed as Britain's first large-scale exhibition of Basquiat, an icon of New York's post-punk underground art scene who died of a heroin overdose in 1988 at the age of 27.
He has had little exposure in Britain, and not a single work of his is held in a public collection.
Banksy shot to prominence through guerrilla art in Bristol, later extended to London, that took a sardonic view of British life, often hurling a barb at corporate greed and rightwing politics.
He gained a global audience in March by unveiling a symbol of the division of the West Bank -- the "Walled-Off Hotel" in Bethlehem, just a few metres from Israel's separation wall.
His identity is a mystery, though there have been frequent attempts to pierce his secrecy.