The Review Show being broadcast this Sunday will be the last, and the end of 20 years of transmission of the show, which began as The Late Review in 1994.
Last year, the show was moved from a weekly slot on BBC2 to a monthly broadcast on BBC4 and commentators had predicted its demise.
The show was made at BBC Scotland's headquarters at Pacific Quay in Glasgow and was presented by Martha Kearney and Kirsty Wark.
The BBC's head of arts, Jonty Claypole, is also based in Glasgow and has commissioned new arts programmes from the site, but the regular review show format appears to be over.
The arts programme is reported to have lost about 80% of its audience following the controversial move to BBC4 in April last year.
Staff working on the show are expected to move to work on other new shows, an industry insider said.
BBC sources said that reviews by critics would still be a part of its arts coverage, but may only be available online in an expanded internet arts package.
Earlier this week Tony Hall, director general of the BBC, said that cultural programmes would be "at the very heart" of the corporation.
A BBC spokeswoman said: "This Sunday's Review Show will be the last.
"The series has made a valuable contribution over many years but as outlined this week, the BBC has ambitious plans for arts on TV, radio and online.
"Review will continue to have a place across the BBC alongside more topical arts coverage."
The show started life as The Late Review in 1994 on BBC2, before being attached to the channel's flagship news programme to become The Newsnight Review in 2001.
Filming of the programme moved to Glasgow in 2010, when it was relaunched as The Review Show.
A BBC Scotland spokesman said: "We are currently in the midst of a raft of arts programming from BBC Scotland, which recently included profiles of graphic artist Frank Quitely, photographer Albert Watson, and review of Stanley Spencer's work on the Clyde shipyards by artist Lachlan Goudie, with further programming to come on the work of Oscar Marzaroli, and Scottish film-makers John Grierson and Norman McLaren as well as specials on the Glasgow School of Art and the Kelpies sculptures.
"The recent BBC-wide arts announcement included a major new series on the history of Scottish art, as well as other ventures involving Scottish Opera and the BBC Scottish Symphony Orchestra."