Mr Stewart, who had four children, had been suffering from cancer and died at home on Thursday.
Bergerac, which ran on the BBC on Sunday nights from 1981 to 1991, brought huge publicity to the Island and made a star of John Nettles as the detective in the title role.
Although there have been regular attempts floated to revive the series, none have come off.
Aside from his work with Bergerac, Mr Stewart also created detective show Shoestring, and produced episodes of programmes such as Hannay, The Darling Buds of May and Lovejoy.
