Laws was appointed on Monday morning after Alan Knill was sacked. He had been in charge of Shamrock for the last seven games of the Irish season.
He had been strongly linked with a move to Hartlepool, with Skybet suspending betting on the market after he was backed in from 10-1 to 1-5.
Laws told BBC Radio Humberside he had three job options, having had to wait since December 2010 until last month to get a return to the game.
"It's crazy isn't it. You wait for something to happen and all of a sudden I had three things happen," he said.
"In Ireland they wanted me to stay and I've spoken to Hartlepool, but my heart was always pulling towards Scunthorpe.
"I'm very proud to have been part of a successful period of the club's history. At the moment I see that falling apart and want to try and help weld it back together.
"It is time to get the staff, supporters and players all united again and get a smile back on their faces. There have been people in and around the football club feeling sorry for themselves, and I can come in and give them some direction."