Windsor Davies died peacefully at his home on Thursday and his daughter Jane later issued a statement following his death.
She said: “They leave a large and very close family who will all remember them with love, laughter and gratitude.”
His cause of death has not been confirmed, and comes after the actor retired to France with his wife of 62 years, Eluned, who died in September.
The couple shared five children together.
Tributes have been pouring in for the actor as fans flocked to Twitter to pay their condolences.
One person wrote: “So sad to hear of Windsor Davies passing. He was a wonderful actor.
“Windsor was so brilliant in it Ain’t Half Hot Mum. RIP Sergeant Major Shut-Up.”
Another person said: “Sad to say Windsor Davies has died. The sound of his ’SHUT UP’ bellowing out of the TV is one of my favourite landmark childhood memories.”