The outing will be the third time Muller has contested the French WRC event. He drove an ORECA-run Citroen World Rally Car in 2010, before switching to a Super 2000 Peugeot last season - which he found frustrating.
"I am really looking forward to competing in my home event in a top level World Rally Car after last year's run in an S2000," said Muller.
"I have only had a day to familiarise myself with the Mini, but the balance of the chassis immediately gave me a great deal of confidence.
"As both my Chevrolet touring car and the Mini use similar 1.6 turbo engines, the performance was nearly the same.
"I am sure it will take me a little while to get used to driving with pace notes again, even so my target would still be a finish in the points."
Team boss Dave Wilcock said he was excited to get a chance to work with Muller after Prodrive had battled against him in touring cars.
"In Prodrive's British Touring Car days in 1998, '99 and 2000 I engineered several cars and we had great battles with Yvan," said Wilcock.
"This will be the first time we have been on the same side.
"He is a tremendously talented driver with great sympathy for a car and I think the Mini WRC chassis will suit him perfectly for the fast flowing stages in France.
"He has competed here twice before and once he has settled in for a few stages I can see him setting some impressive times."
Prodrive has fielded a variety of drivers alongside team regular Dani Sordo this year, including circuit racers Richard Goransson and Eliseo Salazar, plus Patrik Sandell and Pierre Campana.