The musician, real name Daniel Dumile, was known for his rhyme style and his performances in which he always wore a mask.
In a post on the rapper's Instagram account on Thursday, his wife Jasmine confirmed that he died on 31 October.
A number of artists have paid tribute to MF Doom including Run The Jewels and Tyler, The Creator.
In a note addressed to the rapper, his wife paid tribute to "the greatest husband, father, teacher, student, business partner, lover and friend I could ever ask for".
His representatives confirmed his death to Rolling Stone magazine.
MF Doom was born in London but moved to New York as a child.
As a teenager he performed in hip-hop group KMD. Following the loss of his younger brother, he disappeared from music.
But in 1997, he remerged at open mic events wearing tights over his face.
As time went on, he started to wear a mask during his performances based on Doctor Doom, a Marvel super villain.
MF Doom released six solo albums and was also known for his collaborations with musicians such as Danger Mouse and Ghostface Killah.
He made appearances on BBC Radio 4 and Radio 1 in which he discussed his own music and projects with other artists.
Radio presenter Zane Lowe said: "Rest In Peace to the great MF Doom. A true artist who gifted us with eternal innovation and creativity."
Tyler, The Creator wrote on Twitter: "Safe travels villain".
While the Sleaford Mods said: "RIP MF DOOM. Sleep well mate."