Mirren won an Oscar in 2007 for her portrayal of the monarch in the film "The Queen," which Morgan wrote and Stephen Frears directed.
The BBC said "Billy Elliot" director Stephen Daldry will helm Mirren in the West End production next February. The play will be about the longtime queen's dealings with the 12 prime ministers who held office during her reign.
"From Churchill to Cameron, each prime minister has used these private conversations as a sounding board and a confessional -- sometimes intimate, sometimes explosive," a synopsis issued to the BBC said.
Celebrity Families of 2014 [PHOTOS]