The pair will take to the stage as part of the raucous royal affair, which is based on the true story of one of the most audacious heist attempts in British history.
The play tells the story of the unpredictable Colonel Blood and his plan to steal the world-famous jewels, aided by a gang of misfits.
Murray is shown in full royal regalia as the “Merry Monarch” Charles II, with Giedroyc as a French noblewoman.
They also double as married couple, and keepers of The Crown Jewels, Talbot and Mrs Edwards.
Their fellow castmates include Carrie Hope Fletcher, Aidan McArdle, Neil Morrissey, Tanvi Virmani, and Joe Thomas from The Inbetweeners.
The Crown Jewels is written by Bafta-nominated writer Simon Nye, and directed by multi-Olivier Award winner Sean Foley.
The show will play at the Garrick Theatre from July 7 until September 16, ahead of regional dates in the autumn.
Venues include The Lowry theatre in Salford, the Marlowe Theatre in Canterbury and the New Theatre in Cardiff – with additional casting to be announced.
“I hope audiences will be as titillated and thrilled as I am at the prospect of a riotous comedy-drama about a crown jewels heist that really happened,” Nye said.
“True crime comes to the West End, 350 years after the event. The cast is an amazing array of comedy talent, and the subject matter absurdly topical.
“Satire, sword-fighting, love, violence, an examination of the monarchy and Anglo-Irish relations – could you ask for anything more?”
Foley said he was “thrilled” to have the opportunity to direct the play, which “transports us to a completely different time – a time when England had a new king… whose name was Charles”.
“I’m excited to be working with our brilliant cast, and we all hope to thoroughly entertain audiences in one of my favourite theatres – the Garrick – over this Coronation summer,” he said.
The Crown Jewels is produced by Simon Friend in association with Adam Kenwright, Trafalgar Theatre Productions, Jenny King, Gavin Kalin, David Adkin and JAS Productions.