Laws spent almost a decade at Glanford Park before joining the Owls on Monday.
And it was Laws' success at Scunthorpe, who he leaves third in League One, which caught the eye of Allen.
"Brian has served a proper apprenticeshup and is well respected in the game," he said.
"He has good contacts, and I'm sure his best years are ahead of him. I think there are exciting times ahead at Hillsbrough for Laws, his team and everybody involved with the club."
The current Scunthorpe side is lauded as the best seen in North Lincolnshire for many a year, and Allen admits their style of the game helped convince him to opt for the former Nottingham Forest defender.
"After the first interview I was impressed with his views on football," added Allen.
"We had Scunthorpe watched and have seen the type of football they played, and an important factor is that Laws comes from the Brian Clough school.
"I'm a great admirer of Cloughie. Laws likes to play attractive and attacking football, I see Wednesday going forward from here."