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He was also an actor, performer and entertainer, appearing in films and on stage.
"No one deserves to be called a broadcasting legend more than Nicholas Parsons," BBC Director General Tony Hall said in a statement.
"His charm, inventive intellect and ability to create laughs were unsurpassed."
Parsons was best known for Just A Minute, in which panellists have to talk non-stop for 60 seconds on any given topic without hesitation, deviation or repetition.
Gyles Brandreth, a friend who worked with Parsons on the programme said: "It's heartbreakingly sad and it is the end of an era in many ways.
"He was a consummate professional and a role model to so many people because he just went on working right up to when he was 95.
"It's a career truly to celebrate and a man to celebrate," he told the BBC.