The plays, about James I, II and III of Scotland will star Sofie Gråbøl, known to millions of fans as Sarah Lund from The Killing TV detective series, as well as James McArdle and Blythe Duff, among others.
Directed by Laurie Sansom, the artistic director of the National Theatre of Scotland, which is producing the plays, all three will be staged at the EIF in August and then be staged at the National Theatre in London in September.
The trilogy aims to bring to life three generations of kings who ruled Scotland in the tumultuous fifteenth century.
The NTS said: "Each play stands alone as a unique vision of a country tussling with its past and future, with its own distinct theatrical atmosphere. Viewed together they create a complex and compelling narrative on Scottish culture and nationhood.
"The James Plays promise to be historical drama for a contemporary audience, served up with a refreshing modern directness."
Sofie Gråbøl will be acting in English on the stage for the first time, and will play Margaret of Denmark, the wife of James III, who lived from 1452 to 1488.
Ms Sansom said: "When I first read Rona Munro's trilogy of plays about James I, II and III of Scotland, I realised that not only were they a rare gift to an incoming Artistic Director, they were also something extraordinary to offer to audiences during a year when Scotland's history and future are under the spotlight.
"The three plays are daring, passionate and offer a tumultuous ride through Scottish 15th century history.
"I look forward to bringing Rona's vividly evoked backstage dramas of Scotland's medieval royalty to a contemporary audience in a remarkable year for Scotland and friends."
Sir Jonathan Mills, the director of the Edinburgh International Festival said: "Rona Munro's specially commissioned history plays explore a colourful, intriguing and critical period in Scotland's history lived through the lives of three very different monarchs and the ways in which their personalities and political environment shape their times.
Ms Munro said she wrote the plays because she adores medieval history.
"We do not have many accessible, popular culture versions of our medieval history in Scotland and most people have very little knowledge of these events. I want people to experience them as I imagine them, not as something remote happening to people in odd costumes talking in inaccessible 'history speak' but as visceral, epic stories of people who thought and felt as we do," she added.