His family confirmed that he passed away on November 23 and was buried last Thursday. The actor had been ill with vascular dementia for four years.
Mr Sachs was best known for his role as Manuel, the hapless Spanish waiter in the hit 1970s sitcom, Fawlty Towers.
John Cleese, his co-star and co-creator (with Connie Booth) of the show, tweeted: “Just heard about Andy Sachs. Very sad. A very sweet gentle and kind man and a truly great farceur. I could not have found a better Manuel. Inspired.”
A tweet from actress Tracy Ann Oberman read: “Aw RIP #andrewsachs. Worked with him on a number of plays for @BBCRadio4. A lovely lovely man. Talked of his childhood,how it shaped him.”
Sir Tony Robinson, star of the Blackadder series, tweeted: “So sad that Andrew Sachs has died. A true friend and a kindred spirit.”
“Andrew Sachs made me cry with laughter in my favourite sitcom,” wrote Miranda Hart, the actress and comedian. “That legacy won’t die but today a little cry that he and his era have gone.”
Andreas Siegfried Sachs was born in Berlin in 1930. His father, Hans, an insurance broker, was Jewish; his mother, Katharina, a librarian, was a Catholic.
The family fled to London in 1938 after Mr Sachs’s father was arrested by the Nazis and later released.
In an interview with the JC in 2007 Mr Sachs said: “Half of me is Jewish. Sometimes I think it might be the better half.”
After the success of Fawlty Towers, he went on to feature in BBC radio productions, including The Count of Monte Cristo and Neil Gaiman’s Neverwhere.
He also appeared in a number of episodes of ITV’s Coronation Street in 2009.
Jewish aid charity World Jewish Relief expressed its condolences to Mr Sachs’s family. The charity was responsible for bringing the family from Berlin in 1938 and supporting them once they arrived in the UK.
They were among the tens of thousands of people who fled Nazi-occupied Europe who were supported by World Jewish Relief’s predecessor organisation, the Central British Fund for German Jewry.
Rafi Cooper, WJR director of communications, said: “Andrew Sachs was both loved and admired. Like so many who fled Nazi Germany and settled in the UK, he made a significant contribution to British society; he certainly qualifies as a national treasure.”
In 2009, Mr Sachs was the victim of several prank phone calls from comedian Russell Brand and broadcaster Jonathan Ross, which led to the latter’s suspension from the BBC for 12 weeks.