His Oscar-winning father said the family “are all totally bereft” after he died on Saturday.
“I am shattered to have to announce that my beloved elder son Nick died a few hours ago in Basingstoke Hospital,” Lloyd Webber wrote on Twitter.
“His whole family is gathered together and we are all totally bereft.”
Nicholas followed in his father’s footsteps by becoming a composer, scoring the BBC’s Love, Lies And Records, and a theatrical and symphonic version of The Little Prince.
He also produced his father’s Symphonic Suites at the Theatre Royal Drury Lane in London.
He was diagnosed with gastric cancer 18 months ago.
The 75-year-old, best known for musicals including Cats, The Phantom Of The Opera, and Starlight Express, missed the opening of Bad Cinderella at New York’s Imperial Theatre as a result.