Wilcox will now take control of the team, assisted by youth team coach Paul Wilson and physio Nigel Adkins for Saturday's visit of Leyton Orient.
In a message on the club's official website tonight Laws said: "After what has been a very difficult day for me, I think it is fitting that I end it with a message to the supporters.
"I would like to put on record my thanks to all those who have offered kind words. It really does mean a lot to me and my family.
"I have made a lot of good friends at Scunthorpe United and developed positive working relationships with many.
"I now live in Scunthorpe and want to be able to hold my head high around the town. You, the supporters have always been magnificent towards me and I would like to thank you for your backing. All my hard work has been in an attempt to give you a club that you can be proud of.
"I hope that I will be able to meet with some of you around town and visit Glanford Park again in the future.
"It had become like a second home to me and I will miss the job. But as one door closes, another will open for me i'm sure.
"Keep believing, up the Iron"
Iron-Bru.net would like to thank Brian for his hard work on behalf of the club over the past seven years, which has resulted in many memorable moments for fans - notably May 29 1999. Everyone connected with the site wishes him well for the future.