Marshall, who originally owned a music shop in London, founded Marshall Amplification 50 years ago.
Jimi Hendrix and Kurt Cobain are among the musicians who used Marshall amps.
A tribute has been posted on the Marshall website. It reads:
"It is with profound sorrow that we announce the passing of our beloved founder and leader for the past 50 years, Jim Marshall. While mourning the Guv’nor though, we also salute a legendary man who led a full and truly remarkable life.
"Jim’s ascent into the history books as ‘the Father of Loud’ and the man responsible for ‘the Sound of Rock’ is a true rags-to-riches tale.
"Cruelly robbed of his youth by tubercular bones, Jim rose to become one of the four forefathers responsible for creating the tools that allowed rock guitar as we know and love it today to be born.
"The ground-breaking quartet also includes the late, great trio of Leo Fender, Les Paul and Seth Lover – together with Jim, they truly are the cornerstones of all things rock.
"In addition to the creation of the amps chosen by countless guitar heroes and game-changing bands, Jim was also an incredibly humble and generous man who, over the past several decades, has quietly donated many millions of pounds to worthy causes.
"While the entire Marshall Amplification family mourns Jim’s passing and will miss him tremendously, we all feel richer for having known him and are happy in the knowledge that he is now in a much better place which has just got a whole lot louder!
"Rest in Peace and thank you Jim.
"Your memory; the music and joy your amps have brought to countless millions for the past five decades; and that world-famous, omnipresent script logo that proudly bears your name will always live on."