Farke has signed a three-year contract to replace Adi Hutter, who was dismissed at the end of the 2021/2022 season following a disappointing 10th place finish.
This will be Farke's first job in the German top flight, having previously been in charge of Borussia Dortmund's reserve side.
Farke was sacked as Norwich City manager back in November with the club bottom of the Premier League table. He spent your years in charge of the Canaries, leading them to two promotions from the championship.
Farke signed for Russian outfit Krasnodar in January this year but left in March without taking charge of a single game following Russia's invasion of Ukraine.
The Foals' sporting director Roland Virkus told the club website on Saturday: 'In Daniel Farke, we have been able to sign a coach that fits perfectly to the path that we want to go down as a club.
'We are looking forward to tackling the challenges that lie ahead of us, together with him.'
