The "Empire State of Mind" rapper was the anonymous buyer of the painting at a Sotheby's auction in Manhattan last week, the newspaper said.
The work is an orange, white and black acrylic and oil-stick work, featuring the Empire State Building under Basquiat's signature crown symbol, the Post said.
Basquiat died of a heroin overdose in 1988. He was 27.
2014: The Year in Music [PHOTOS]