The marathon, which can be streamed over the BBC's web site, marks the 60th anniversary of the day the composer stepped outside his house to smoke a cigar and was shot and killed by a U. S. military cook.
Webern's oeuvre, which takes about five and a half hours to play, will be played in order of composition, with commentary from guests such as biographers Malcolm Hayes and Katherine Bailey, and composer Julian Johnson.
In the evening, a panel will discuss the composer's life and works.
Webern, a student of Arnold Schoenberg, was a member of the Second Viennese School, a group of composers that made use of Schoenberg's twelve-tone technique.
For more information about Webern Day, go to www.bbc.co.uk.