The pair are among 18 film-makers vying for the prestigious Palme d'Or at the annual film industry get-together in the south of France.
Loach's Jimmy's Hall is based on the true story of an Irish communist who ran a dance hall, while Leigh's Mr Turner is a biopic of the painter JMW Turner with his regular collaborator Timothy Spall in the title role.
Both Loach and Leigh are regulars at the festival and previous winners of the Palme d'Or.
Leigh won it in 1996 for Secrets and Lies, while another of Loach's films set in Ireland - The Wind That Shakes the Barley - won a decade later.
Jimmy's Hall will be Loach's 18th film to be shown at Cannes since he made his first appearance there in 1970 with Kes.
The festival, which is held next month, opens with a Grace Kelly biopic called Grace of Monaco starring Nicole Kidman as the princess and Tim Roth as her husband, Prince Rainier.
The pair married after meeting at the festival in 1955, but the film concentrates on her life after the wedding.
Other films in the running include Tommy Lee Jones's western The Homesman starring Meryl Streep and Hilary Swank and wrestling drama Foxcatcher with Channing Tatum, Mark Ruffalo and Sienna Miller among the cast.
Michel Hazanavicius, the man behind the Oscar-winning The Artist, is also in competition with his new film The Search.
Other films being shown out of competition include Ned Benson's Eleanor Rigby, which stars Jessica Chastain and James McAvoy, and Ryan Gosling's directorial debut Lost River.
Director Jane Campion, the only woman to have won the Palme d'Or, is leading the festival's jury this year for the competition on the Riviera resort.
Tessa Ross, controller of film and drama at Channel 4 which backed both films, said: "I'm delighted that two of our most significant film-makers will premiere their latest films side by side on the Croisette.
"Ken and Mike are synonymous with great British film-making; with Jimmy's Hall and Mr Turner they return to Cannes with two wonderful films which join their extraordinary canon of work. We're privileged to have supported them both."