The appointment represents a remarkable transformation of fortunes for the 48-year-old, who was sacked by Championship strugglers Wednesday just last month.
Laws, who began his playing career with the club in 1979, will be joined there by his former Wednesday assistant Russ Wilcox.
Veteran captain Graham Alexander, 38, has also been handed a new role as a player-coach.
The new coaching team is set to be unveiled at a press conference at the ground at 3:30pm on Wednesday.
A club statement read: "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."
Burnley have acted quickly following the departure of Coyle and most of his backroom staff.
Doncaster boss Sean O'Driscoll was initially thought to be the front-runner for the position but the Championship club issued a statement this morning saying their manager would not be leaving South Yorkshire.
That left Laws as the preferred choice and Burnley believe they have found the right man despite the poor form of Wednesday earlier this season that led to his departure from Hillsborough.
The statement added: "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."
Laws took over at cash-strapped Wednesday in 2006 and kept the club in the Championship, earning a respectable mid-table finish last season.
After enjoying his best playing years at Nottingham Forest, he began his managerial career at Grimsby, where his tenure is best remembered for a remarkable incident when he threw a plate of chicken wings at player Ivano Bonetti.
He went on to guide Scunthorpe to promotion twice over the course of almost 10 years, but his time there was not without incident as he was sacked amid a power struggle in 2004 only to be reinstated three weeks later.
Laws' task will be to make sure the Clarets' first Premier League campaign does not end in relegation. They are currently just two points above the bottom three.
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