After days of talks, the two parties have reached an agreement over an initial compensation fee of €12m (£10.2m).
The Belgian, who is expected to be unveiled next week, has agreed a three-year contract at the Allianz Arena as he takes over from Thomas Tuchel.
The fee Bayern have agreed to pay is the highest in Burnley’s history, but it also ranks the highest fees paid in footballing history too.
Here, we take a look at where Kompany’s £10.2m compensation ranks among the highest fees for football managers:
1. Unai Emery (Aston Villa) - £5m
It was money well spent as Villa forked out £5m to bring Emery from Spanish side Villareal in 2022. Photo: Alex Davidson
2. Ronald Koeman (Everton) - £5m
The Toffees paid out the same fee to bring the Dutchman to Goodison Park from Southampton in 2016. Photo: Tony Marshall
3. Jose Mourinho (Chelsea) - £5m
The self-dubbed 'special one' was prised away from Porto in 2004. Adjusted for inflation, that fee would be around £8.5m today. Photo: Mike Hewitt
4. Maurizio Sarri (Chelsea) - £5m
The Italian made the move to Stamford Bridge from Napoli in 2018. Photo: Dan Mullan