Laws, who left Glanford Park to take charge of Sheffield Wednesday in November 2006, edged out the Doncaster boss Sean O’Driscoll to the post.
Russ Wilcox, Laws' assistant at Glanford Park and Hillsborough, will resume his role while Graham Alexander, himself a former Scunthorpe player, will become a player-coach.
“We believe Brian will deliver a continuity of the culture to which Burnley fans and staff have become accustomed,” read a statement from the club.
“His 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 this stability is maintained over the next few years, Brian has demonstrated great loyalty having managed just three clubs in total and two in the last 13 years.”
Laws is a former Clarets player, having started his career at Turf Moor, but it remains a surprise that he could take charge of a Premier League side having been sacked by Wednesday only last month.
He steered the Iron to promotion from Division Three as play-off winners in 1999 and League Two – as the fourth division was rebranded by then - as runners-up in 2004-05. He left in November 2006 with the Iron top of the table, with Nigel Adkins going on to lead United to only their second title since entering the Football League in 1950.
Laws had twice been in the running to be Burnley manager, according to our sister site Clarets MAD, and after impressing their chairman Barry Kilby at an interview on Sunday.
In 1996 he missed out to Adrian Heath, and in 2007 Wednesday denied the club permission to talk to him. They instead appointed Owen Coyle, who led them to promotion via victory in the Championship play-offs last season before leaving to take charge of Bolton Wanderers.