London gallery Gimpel Fils said that the painter died peacefully at home on Saturday.
Davie's work is being displayed at Tate Britain later this month as part of its BP Spotlights series, which offer more depth on specific artists or themes.
The Tate said that he was one of the first British artists after the war to develop an expressive form of abstraction, creating "kaleidoscopic canvases".
It described the works as "the result of an improvisatory process that the artist relates to his love of jazz".
In a statement on its website, Gimpel Fils said: "It is with great sadness we announce that Alan Davie died peacefully at home on Saturday 5th April.
"Details of a memorial event will follow in due course."
It is holding an exhibition of his work later in April.
Davie was born in Grangemouth in Scotland in 1920 and attended Edinburgh College of Art.
He worked as a jazz musician and also made jewellery during the 1940s.
During his career as an artist his work featured in exhibitions around the world, from South America to Australia.
The Barbican in London and the National Gallery of Modern Art in Edinburgh are among those which have held retrospectives of his work.
In 1991 he became a Senior Fellow of the Royal College of Art in London.