The Upstairs Downstairs actor, who was a regular guest star in Holmfirth sitcom Last of the Summer Wine, died on January 3.
The news was announced by Mr Beeny's son, Rick Blackman, on Twitter on Wednesday.
He tweeted: "I have some sad news to impart. On friday 3rd of January my old dad Christopher Beeny died at his home in Kent. He was 78. Comforted to know he was not alone at the end and was in his armchair".
Beeny was best known for playing butler Edward Barnes in TV series Upstairs Downstairs.
The popular series, which aired in the 1970s and was a ratings hit for ITV, told the story of Lord and Lady Bellamy and their upper crust household at 165 Eaton Place in Belgravia.
He also appeared In Loving Memory as Billy Henshaw opposite Dame Thora Hird and as Lenny Grove in The Grove Family.
He was also a regular guest star on Last Of The Summer Wine until 2009, when he joined the cast.
His screen debut was in The Long Memory in 1953, also opposite Dame Thora, after he trained at the Royal Academy Of Dramatic Art.
He went on to make regular appearance in the theatre, including in Stop The World - I Want To Get Off, Oliver! and Boeing Boeing and he toured the play There's No Place Like A Home with 'Allo 'Allo's Gorden Kaye.