The retired Belgium international, 36, who was in charge at Anderlecht until last month, said he was “excited by the challenge ahead”.
“Burnley Football Club is a truly historic English side and it is an honour to be appointed first-team manager,” said Kompany, who takes over from caretaker Mike Jackson.
Jackson replaced long-serving boss Sean Dyche in April but could not save the club from relegation to the second-tier Championship.
“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,” said former defender Kompany.
“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 spent 11 years at City, where he won 10 major trophies, including four Premier League titles.
He returned in 2019 to Anderlecht, the club where he launched his career, as player-manager but relinquished matchday duties after a disastrous start to the season.
Kompany retired as a player in 2020 and took over as head coach.
Burnley chairman Alan Pace said the Clarets had signed up a “proven leader”.
“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,” he said.
“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.”
AFP