Croft, whose TV credits include classics Dad's Army and Hi-de-Hi!, passed away this morning.
A message on his official website reads: "The family of comedy legend David Croft OBE are sad to report that David died peacefully in his sleep at his house in Portugal earlier today.
"He was a truly great man, who will be missed by all who had the great fortune of knowing and loving him. We know that he would have been proud that you had all been watching."
> David Croft: Five of his best TV shows - video
Croft, real name David John Sharland, was born in 1922 to actress Annie Croft and radio star Reginald Sharland.
He served in the army between 1942 and 1947 in England, India, Singapore and North Africa, which inspired his later works Dad's Army, 'Allo 'Allo! and It Ain't Half Hot Mum.
In his early days at the BBC and Tyne Tees Television, Croft helped produce and direct a number of hit comedies such as The Benny Hill Show, Steptoe & Son and Beggar My Neighbour.
During work on the latter, he first crossed paths with long-term collaborator Jimmy Perry. Together, Perry and Croft became two of the most renowned and loved comic writers in the country, producing Dad's Army, It Ain't Half Hot Mum, Hi-de-Hi! and You Rang, M'Lord?.
His final work was a pilot for Here Comes The Queen, which featured Wendy Richard and Ian Lavender, aired in 2008.
In 1978, Croft was awarded an OBE for services to television. He also won a 'Desmond Davis Award' for his outstanding contribution to the TV industry and a 'Lifetime Achievement Award' at the British Comedy Awards.
Croft's comedy was loved and celebrated for its warm, family-friendly nature and his clever wordplay.
In an interview with the TV Times in 2004, Croft complained that modern comedy had become too smutty and youth-orientated.
"There's no double entendres, it's single entendres - which alienate large parts of the public," he said.
"In my day you wrote a show and if it was funny it found its audience... Everyone aims for the 18-25 age group, but they're at the pub or the latest movie."
Watch a classic David Croft moment on Dad's Army:
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