His agent says the 83 year old died after a short illness
Born in Croydon in south London, Hudd was best known for his radio satirical series The News Huddlines, which ran from 1975 to 2001.
A statement from his agent said: "We are sad to announce the passing of the much-loved and amazingly talented Roy Hudd OBE.
"After a short illness, Roy passed away peacefully on the afternoon of Sunday the 15 March, with his wife Debbie at his side.
"The family would ask you to respect their privacy at this very sad time."
Hudd broke into television in the mid-1960s in sketch series including The Illustrated Weekly Hudd and The Roy Hudd Show and was also an authority on the history of music hall entertainment.
Across his varied career he also appeared in ITV soap Coronation Street as undertaker Archie Shuttleworth, as well as Call The Midwife, Holby City and Midsomer Murders.
In recent years, Hudd played Bud Flanagan in the BBC drama We're Doomed! The Dad's Army Story and appeared in the ITV series Broadchurch in 2017.