The works, marking the opening of an exhibition by American artist Jean-Michel Basquiat, appeared in a tunnel close to the Barbican Centre in central London.
Banksy described the murals as an “(unofficial) collaboration” in a series of Instagram posts.
Basquiat first rose to fame as a New York City graffiti artist before turning his hand to painting. He died in 1988, aged just 27, from a suspected drug overdose, PA reported.
Alongside an image on Instagram of the first work – a Ferris wheel – Banksy wrote: “Major new Basquiat show opens at the Barbican – a place that is normally very keen to clean any graffiti from its walls.”
The second mural, which bears a likeness to Basquiat’s 1982 work Boy and Dog in a Johnnypump, is captioned: “Portrait of Basquiat being welcomed by the Metropolitan Police – an (unofficial) collaboration with the new Basquiat show.”
Basquiat: Boom for Real opens at the Barbican Centre on Wednesday.
It has been described by the arts venue as the “first large-scale exhibition in the UK of the work of [the] American artist”.
Banksy is thought have been born in Bristol, just 20 miles north west of Weston-super-Mare - where he based a 2015 attraction - in the early 1970s.
The artist may have run with one of the city’s prolific graffiti gangs, but Banksy’s own work grew to prominence in the 1990s.