The screening this Thursday at the Queen Elizabeth Hall in the South Bank is part of the 10th anniversary celebrations of the Ether festival, which features cutting-edge acts from past and present.
The event has already featured the debut of Gregory's opera, Piccard in Space.
Utley and Gregory will perform their soundtrack as part of an eclectic group built around electric guitars and voices, supplied by the Monteverdi Choir, and led by celebrated conductor Charles Hazlewood.
Dreyer was a pioneering film-maker and Joan of Arc represents what was a big step forward at the time with its experimentation in film tone and powerful use of close-ups.
Its naturalistic style has lent itself to many forms of musical interpretation, from major symphonic work to a Nick Cave soundtrack in 1995.
Utley said he and Gregory watched a series of films at Bristol's Watershed arts centre before settling on the film.
"We have tried to do is to create something that fits the film, with a feel that is medieval and contemporary," he told Music Week.
"We have tried to be respectful to the film-maker, not creating something forced, like putting a dubstep soundtrack over Battleship Potemkin, and we have also tried to steer away from the traditional silent film piano score."
The soundtrack was commissioned by Bristol's Colston Hall, where it premiered last year.
For more information and tickets, go to: http://ether.southbankcentre.co.uk/