He is understood to have contracted an autoimmune disease and suffered a heart attack last week.
Gillett was the BBC Radio 3 World on 3 presenter and host of the BBC World Service programme Charlie Gillett's World of Music.
He was an ardent and long time champion of many Nonesuch artists. He provided exposure to renowned performers such as Youssou N'Dour, Oumou Sangare, and Rokia Traoré.
Gillett is also credited with discovering the British Rock band 'Dire Straits' in 1976. He wrote an acclaimed history of rock 'n' roll, The Sound of the City, in the 1970s.