Laws, 50, has been out of work since being sacked by Burnley in December 2010.
Shamrock are without a manager as Stephen Kenny was sacked last week following a derby loss to Bohemians.
Laws will take charge of the first-team for seven games until the end of the season, while the club's board of directors decide on a permanent appointment.
“We have six important league games and the EA Sports Cup final coming up over the next month and a half, and Brian is coming in to help the existing back room staff to do as well as possible in those games," said Shamrock chairman Jonathan Roche.
"Bringing Brian in also gives the club some breathing space to take our time to pick the next manager. Brian’s experience in the game will help us very much in the short term, and he has recruited many players from Ireland so he is not a stranger to the league.”
Laws becomes the second former Iron boss in the Republic of Ireland's top flight, with Ian Baraclough's Sligo Rovers seemingly on course for their first title in 35 years in his first season with the club.
Shamrock had been favourites for the title, but trail Baraclough's outfit by 13 points.
Laws took charge of the Iron in 1997, following the departure of Mick Buxton. He led the team to promotion to Division Two (now League One) via the play-offs, but quit in 2004 with relegation out of the Football League a real possibility.
He was re-installed after a boardroom coup led by majority shareholder Steve Wharton, who returned as chairman, and in 2005 secured promotion back to the third tier after finishing second in League Two.
He left to take charge of the Championship side Sheffield Wednesday in November 2006, but his time in charge at Hillsborough was brought to an end with the Owls sliding towards relegation in 2009.
A brief spell in charge of Burnley the following season also brought the drop, although the Clarets were already on course to exit the Premier League before his appointment.
"I have significant football managerial experience having taken charge of over 800 league games in all four divisions in England. I aim to bring that experience with me to advise, guide and lead the club’s short-term strategy," said Laws.
"My strengths include getting to know clubs from top to bottom and leading change where necessary, at all times identifying and building on the club’s strengths, culture and brand. I am delighted to be accepting the challenge and can't wait to get going.”