Brazilian di Grassi, 29, has been a member of the German manufacturer’s World Endurance Championship line-up since late last year and finished third at the Le Mans 24 Hours sharing an R18 e-tron quattro with Marc Gene and Oliver Jarvis.
He made 19 grand prix starts for Virgin in 2010 with a best finish of 14th in Malaysia.
Muller, meanwhile, lies seventh in the FR3.5 standings, having taken his maiden series victory in the Monaco Grand Prix support race this year.
He has also been a race winner in GP3 and a podium finisher in the Formula Renault Eurocup.
“We are intrigued to see just how Nico and Lucas get to grips with our RS 5 DTM,” said Audi DTM chief Dieter Gass.
“Nico is a promising young driver whose career we have followed with great interest for some years now.
“Lucas, meanwhile, has impressed our sportscar team with his speed and knowledgeable technical feedback, which is why he is regarded as excellent test driver.”
Both will drive current-specification RS5s at the Austrian circuit.
Muller tested an old-generation A4 as part of a young-driver evaluation by Audi at Monteblanco last year alongside Red Bull Juniors Carlos Sainz Jr, Tom Blomqvist, Superstars champion Johan Kristoffersson and others.