The arts festival, a partnership between Redford, Sundance Institute and AEG Europe, will bring a taste of Utah's annual Sundance Film Festival to the UK on April 26.
The event will open with 'An Evening with Robert Redford and T Bone Burnett', in which the pair will discuss the classic musical moments in their careers and the films that inspire them. Author Nick Hornby will moderate the discussion, while a special musical guest is still to be announced.
Redford said: "The depth of T Bone's experience and accomplishments in the worlds of both film and music set the stage for the Sundance London programme and the celebration of music and film that's to come.
"His ability to deepen the experience of watching a film through the addition of music has seen him produce and curate some of cinema's most notable and commercially successful soundtracks."
The Sundance Film Festival has premiered indie hits such as Blue Valentine, Winter's Bone, Like Crazy and Martha Marcy May Marlene.
Sundance London will take place from April 26 to April 29, 2012 and feature UK premieres of films from January's 2012 Sundance Film Festival.
Live music performances, discussions, panels and other public events will be held at the four-day festival.
Tickets for both film and music events at Sundance London will go on sale on Monday, November 28 at Sundance-London.com.