Andrew Lloyd Webber said he was "totally bereft" to reveal that his eldest son, Nicholas, had died on Saturday.
The Oscar-winning composer, 75, said the 43-year-old had lost his battle with gastric cancer after he said on Thursday he had been taken into a hospice.
Nicholas had been ill for 18 months.
Andrew in a statement he tweeted tonight said: "I am shattered to have to announce that my beloved elder son Nick died a few hours ago in Basingstoke Hospital.
"His whole family is gathered together and we are all totally bereft."
Nicholas, who was also a composer, had hits including The Little Prince along with producing his father's Symphonic Suites at the Theatre Royal Drury Lane in London to his name.
He was also nominated for a Grammy for musical theatre album alongside his father, Greg Wells and David Zippel for Lord Lloyd-Webber's Cinderella.
Nicholas also scored the 2021 feature film The Last Bus, which starred Timothy Spall and Phyllis Logan and was directed by Gillies McKinnon.
He married viola player Polly Wiltshire during 2018.
The news follows a video posted to Lord Lloyd-Webber's Instagram account on Thursday, in which the composer said his son was "over the worst of this first bout of pneumonia" which he caught as a result of his "ghastly" cancer.
Lord Lloyd-Webber - who wrote the music for hit shows such as Cats, The Phantom Of The Opera and Jesus Christ Superstar - said in a video on Instagram: "We're all here and the family here has gathered around and it was the right place for us all to be I think."
In the video he also thanked the people of Ukraine who sent him a Cats T-shirt following the announcement that his son was "critically ill".
He said: "I know that they've been performing Cats there in a bunker, a makeshift production.
"It's incredibly moving ... everything they're going through they have been so incredibly thoughtful about dearest Nick.
"I'm going to go and see Nick in a minute, and I'm going to pass on all of the fantastic wishes that I've had for him all the way from everywhere all around the world."
Lord Lloyd-Webber also sent his best wishes "to the other families I have around the world in theatre" on the opening night of his new show Bad Cinderella in New York.
He said: "I'm absolutely gutted not to be able to be there but my place is really here in England at the moment."
The Broadway show is a retooled version of London West End's Cinderella, which takes its name from a key song in the show and has new songs, leading lady and title.
Lord Lloyd-Webber's first wife, Sarah Hugill, is the mother of Nicholas. They also share a daughter, Imogen.
