Laws, a former Burnley defender, managed Championship side Sheffield Wednesday before being axed in December.
He faces a baptism of fire, with Burnley playing champions Manchester United at Old Trafford in the Premier League on Saturday with a visit to Bolton looming on January 26.
Laws, presented to the media at a news conference at Turf Moor on Wednesday, said he would do everything he could to bring success and was fully aware he had to operate on a limited budget that is much smaller than many of their rivals.
"We all know that Burnley are not going to be matching a lot of the teams in the Premiership, the likes of Manchester United, we know that," he said.
"But what we will have is prudence and we will make sure we do our work diligently. We'll get players in at the right price and the right time and hopefully (that will) keep us in the Premiership.
"That's the most important thing and we believe we will do that."
Burnley made a bright start to their first season in the top flight since 1976 but have gone nine league matches without a win and have slipped to 14th in the table - just two points above the relegation zone.
Burnley chairman Barry Kilby added the 48-year-old Laws had always been their first choice to fill the vacancy and praised his ability to get results on a tight budget.
"He stands out, he works very well and understands the ethos of this club. Being an ex-player he has an affection for us as well. Being the size we are we have to work within our budget, so its an exact fit."
Kilby said the board were particularly impressed by the way Laws 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 club said on its website:
"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."
Russ Wilcox, 45, who worked with Laws as assistant manager at Scunthorpe United and Sheffield Wednesday will continue as his assistant.
First team midfielder Graham Alexander, at 38 the oldest outfield player in the Premier League, has been appointed player/coach.
Burnley said Laws' arrival would enable the club to build on the foundations laid by Coyle in taking them back to the top flight.
