The actors will be shooting scenes for the comedy drama about an art heist, with Prime Studios hosting production as well as locations in Bradford, it is understood.
Official details about the beginning of production are due to be released later this week.
A tweet from Prime Studios, which is based on Kirkstall Road in Leeds, reads: "Kicking off 2020 by welcoming some high rollers to town, as feature #film #TheDuke heads out to shoot from their #Yorkshire production base @primestudios this week. The art heist comedy drama stars#FionnWhitehead #JimBroadbent & #HelenMirren."
Screen Yorkshire, the region's film and TV agency, has been involved with bringing the production to the region.
In the film which is set in 1961, and directed by Roger Michell, 60-year-old taxi driver Kempton Bunton steals Spanish painter Francisco Goya's portrait of the Duke of Wellington from the National Gallery in London.
While Dame Helen, who was honoured with her DBE in 2003, and Broadbent, who is from Lincolnshire, are known screen veterans, 22-year-old Whitehead won fame more recently as the lead in Christopher Nolan's acclaimed Dunkirk in 2017.
The production is another feather in the cap of the major growth of screen industry activities across Yorkshire.
The film will be presented to buyers at the upcoming American Film Market and will also shoot in London, according to the Screen Daily website.