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:
9. Brendan Rodgers (Leicester City) - £9m
The Foxes were forced to fork out £9m to bring Rodgers south of the border from Celtic. Photo: Alex Davidson
10. Vincent Kompany (Bayern Munich) - £10.2m
Quite staggeringly, Burnley are about to receive the fourth highest fee for a manager in history just a week after relegation from the Premier League was confirmed. Photo: Julian Finney
11. Andre Villas-Boas (Chelsea) - £12.7m
The Portuguese coach was brought to Stamford Bridge from Porto in 2011. Within a year, he had been potted with Chelsea forced to pay out £11.5m to dispense of his services. Photo: Jamie McDonald
12. Graham Potter (Chelsea) - £15m
Chelsea met Potter's release clause in 2022 to take him away from Brighton. Recent financial accounts show Chelsea actually paid £21.5m in total for Potter and his coaching staff. Photo: Clive Rose