The producer died on Friday in a Nashville hospice, said Charlie McCoy, a veteran studio musician who often worked with him.
Johnston worked with Dylan on several albums in Nashville, most notably "Blonde on Blonde." The 1966 album's opening track, "Rainy Day Women #12 & 35," achieved notoriety for its repeated phrase: "Everybody must get stoned."
Rolling Stone magazine ranks "Blonde on Blonde" as the ninth greatest album of all time.