The 48-year-old is thought to have beaten off competition from Doncaster's Sean O'Driscoll to land his first Premier League job, although his arrival appears to have met with a lukewarm reaction from fans.
Laws told the club's official website: "I am sure there are a lot of Burnley fans asking, 'Why Brian Laws?'
"Well let me tell you, I have followed Burnley since I was 16 years old, when I joined the club.
"I have had an affinity with this club for a long time and I am really honoured to have the privilege of managing Burnley Football Club in the Premier League.
"This is a fantastic opportunity. Owen Coyle has done a fantastic job at this club. Nobody can ever take that away and I wouldn't want to even try.
"But at this moment in time he has dropped the baton and we want to pick it up with the supporters and drive on over the finishing line, which means we will have stayed in the Premier League.
"That is our drive and ambition and I will do everything in my power to achieve that because this great club is where it should be."
Laws began his playing career at Burnley in 1979 before moving on to Huddersfield, Middlesbrough and Nottingham Forest, where he enjoyed his best years.
He then cut his managerial teeth as player-boss at Grimsby before taking over at Scunthorpe.
After almost 10 years at Glanford Park, he then moved to Hillsborough in 2006 and kept the cash-strapped Owls in the Championship despite their lack of resources.
He guided them to a mid-table finish last season but then paid the price for a poor start to the current season and was sacked before Christmas.
That has not concerned Burnley, who are convinced they have got the right man.
A statement read: "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."
There is no doubt Laws is an experienced manager having taken over at Grimsby in 1994, although his time there is best remembered for the plate of chicken wings he threw at player Ivano Bonetti.
He went on to guide Scunthorpe to promotion twice in almost 10 years at Glanford Park, but there was controversy there too when he was sacked and then reinstated amid a power struggle in 2004.
Nevertheless, his appointment represents a remarkable transformation of fortunes for someone who endured chants of, "You don't know what you're doing" just weeks ago.
Laws added: "I am a workaholic and I have plied my trade in all the divisions.
"Even though I am only 48, I feel I have a lot of game under my belt and a lot of experience.
"The only area I have to get experience as a manager is in the top flight. However, you have to start somewhere.
"I have only had two jobs in the last 13 years and I have been consistent through that period.
"This is the first time I have been out of work in 30 years, so that tells you I must have something."
With Coyle having taken most of his backroom staff with him after leaving for Bolton last week, Burnley have appointed quickly.
Laws will be joined by his former Scunthorpe and Wednesday assistant Russ Wilcox while veteran captain Graham Alexander, 38, will take up a new role as player-coach.
Laws' appointment appeared inevitable after Doncaster issued a statement this morning insisting O'Driscoll, his chief rival, would be staying in South Yorkshire.
He is due to be formally unveiled at a press conference on Wednesday afternoon.