Kompany, who made 360 appearances for City during 11 seasons at the Etihad Stadium, recently left Anderlecht before taking the Burnley job.
The 36-year-old guided Anderlecht to a third and fourth-place finish in Belgium’s top flight in his two campaigns in charge at Lotto Park.
Speaking about his appointment on the Clarets’ official website, Kompany said: “Burnley Football Club is a truly historic English side and it is an honour to be appointed first-team manager.
“I’m excited by the challenge ahead. I’m looking forward to getting to work with the players and creating a positive, winning team for our fans when we return to Turf Moor.
“I’ve been impressed by the Board’s vision for the club which aligns with my own and I look forward to playing my part as we enter an important season.”
Kompany will have a tough task on his hands to guide Burnley to the Premier League at the first time of asking after their relegation from the top flight last season.
However, there’s no denying he has the leadership qualities to motivate and lead teams to success with the former centre-back lifting 13 trophies - 12 of which while wearing the captain’s armband - during his time in Manchester.
Alan Pearce, Chairman of Burnley said the following on Kompany’s appointment: “We are absolutely delighted to welcome Vincent to Burnley Football Club.
“Vincent is a proven leader and I’ve been very impressed with his ideas for Burnley Football Club, his appetite to succeed and his focus on leading the Club back to the Premier League.
“Vincent has shown impressive credentials in leading one of Belgium’s biggest teams back to European football and a Cup Final last season and we’ve been excited by his philosophy, approach and ambition for the Club.”