The 38-year-old has signed a three-year contract at the Allianz Arena after moving on from Turf Moor after two seasons.
His assistant Craig Bellamy has been placed in temporary charge while the club identifies a permanent replacement, with Mike Jackson his number two.
But who will get the job on a full-time basis?
Here are the current favourites, according to Skybet:
(Odds were correct at the time of writing)
But who will get the job on a full-time basis?
![The Belgian is currently in work at Rangers, where he lost out to Celtic in both the league and cup. Formerly of Genk, Club Brugge and Monaco.](https://www.burnleyexpress.net/webimg/b25lY21zOjkzZDIzYmI2LTUwOTktNDFiOS04MDc2LWIwNzcwODdiMmRlMTowOWViY2I1Yy1jZmZjLTQ4N2YtOTc4Zi1hNDI4ZDdkMjg0MDQ=.jpg?crop=3:2&trim=&width=640)
9. Philippe Clement - 25/1
The Belgian is currently in work at Rangers, where he lost out to Celtic in both the league and cup. Formerly of Genk, Club Brugge and Monaco.Photo: Ian MacNicol
![Has previous experience of leading the Clarets during his caretaker spell during the 2021/22 season. Staying with the club to assist interim head coach Craig Bellamy.](https://www.burnleyexpress.net/webimg/b25lY21zOjRmN2RkZDY4LWJiNzAtNDQ2Ni05NjExLWM2YjJiMWQ3YTA3MTpmOTE3ZTQyYS00YmRhLTQ3NTQtOTE3Ny1jMTE5ZDY1MDlkNjc=.jpg?crop=3:2&trim=&width=640)
10. Mike Jackson - 25/1
Has previous experience of leading the Clarets during his caretaker spell during the 2021/22 season. Staying with the club to assist interim head coach Craig Bellamy.Photo: LINDSEY PARNABY
![Has constantly overperformed with Coventry but has yet to get his break with a bigger club higher up the foodchain.](https://www.burnleyexpress.net/webimg/b25lY21zOmRmMzIzMjMwLThjNTgtNGNlYi05ZDFhLTRkZmM2ZDk5NTQwNDo2ZWQxZjY1YS1mMWVkLTRjZTgtOGMyOC1hN2I1ODg1ZmJlMDI=.jpg?crop=3:2&trim=&width=640)
11. Mark Robins
Has constantly overperformed with Coventry but has yet to get his break with a bigger club higher up the foodchain.Photo: Dan Mullan
![The Argentinian is currently in charge of Saudi side Al-Ittihad, having previously managed Nacional and River Plate.](https://www.burnleyexpress.net/webimg/b25lY21zOjUzNDc3ZjJiLWQ0ZGItNGI5OC05ZTg5LWQwOWE3NjFjNjFiMzozM2VjOThkOC1lMWIzLTQ3ZmYtYjQ4Yy01ODg3OWNiYWNkN2M=.jpg?crop=3:2&trim=&width=640)
12. Marcelo Gallardo - 20/1
The Argentinian is currently in charge of Saudi side Al-Ittihad, having previously managed Nacional and River Plate.Photo: Yasser Bakhsh