Parker has replaced Vincent Kompany at Turf Moor following the Belgian's move to Bayern Munich.
Burnley suffered relegation from the Premier League in 2023/24 after just one season back in the English top flight.
The former England international, who last worked at Club Brugge, will be tasked with leading the Clarets back to the Premier Leauge, a feat he achieved with both Fulham and Bournemouth.
"I'm really pleased to be here," said Parker. "I have been speaking with Burnley for some time now which has been a positive thing as I've now got a real feel for the people around the club.
"To be around the training ground now you start to get that feeling again and I can't wait to get on the training field and start work."
Chairman Alan Pace added: "We are thrilled to welcome Scott to Burnley.
"His vision for the future aligns with our goals and ambitions of returning to the Premier League as soon as possible."
Parker will begin his reign with a Championship match against Luton on August 12th.