The former Sheffield Wednesday boss has signed a two-and-a-half year deal with Burnley and will succeed Owen Coyle.
Laws face a trip to Old Trafford to face Manchester United on Saturday in his first game in charge.
A statement on the club’s official website said: “The Burnley board have been particularly impressed by the way Brian consistently achieved relative success in his former post at Sheffield Wednesday, while operating with one of the lowest wage and transfer budgets in the Championship.
“The results of a Deloitte and Touche study, delivered at the club’s request, confirm that he was top of the list of Championship managers over the period 2006-2009, in terms of delivering the best results relative to financial budgets.
“We believe Brian will deliver a continuity of the culture to which Burnley fans and staff have become accustomed.
“As a former Burnley defender, he is especially familiar with the club, the traditions we have and the passion we all share.
“To aid this continuity, Brian will be assisted in his managerial role by respected midfielder Graham Alexander, who takes up the post of player/coach with immediate effect, as a vibrant and strong management team takes shape.
“Brian’s welcome appointment will provide real stability and enable Burnley Football Club to build on the foundations we now enjoy as a Premier League club.
“It is imperative that this stability is maintained over the next few years and Brian has demonstrated great loyalty, having managed just three clubs in total and two in the last 13 years.”
The statement added: “Brian has shown great acumen with regard to player recruitment, having managed teams with nominal spending and wage budgets and establishing good working relationships with the very top clubs in English football.
“His appointment also dovetails with Burnley’s long established and proud policy of developing home-grown talent.
“During his tenure at Sheffield Wednesday, Brian was steadfast in his determination to blood young talent, giving debuts to eight Academy starlets.
“Finally, the Burnley board of directors are convinced that Laws, who started his playing career at Turf Moor, is a winner who is passionate about returning to manage his former club.
“In closing, we welcome Brian ‘home’ to Turf Moor and we look forward to a long and successful working relationship.”
