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He told the Scunthorpe Telegraph: "I am sure he will be a significant signing for this club.
"He can be as influential for us up front as Peter Beagrie was when he first joined us.
"I've heard it whispered that he is knackered but I've spoken to plenty of people who say he could prove a great signing for us.
"He has turned down the chance to stay at Sheffield United on the coaching staff because he wants to continue as a player.
"He has played all his career in the top divisions, he has never before played as low as this level.
"He still has quality, there is no doubt about that - and he can help us keep possession up front.
"He does not give the ball away easily and that is something that's going to be vital for us this coming season.
"We need the added experience that Tommy Johnson can bring to our squad. Bringing him in is not a gamble, I am delighted to have got him."
Laws also revealed that the Iron have already got a replacement lined up for young striker Andy Parton, who has left for Conference North outfit Stalybridge Celtic.
Meanwhile Sheffield United boss Neil Warnock, for whom Johnson made one appearance towards the back end of last season, believes Laws has pulled off a masterstroke of a signing.
Warnock said: "He will be a good signing for Scunthorpe. He is an excellent professional, a proven finisher in front of goal, and he still has that extra yard of pace every goalscorer needs.
"I spoke to Brian about him a few weeks ago, and I couldn't recommend Tommy highly enough to him.
"He will definitely score goals in League One, and I told Brian that.
"I wanted him to stay here and coach my strikers but he was desperate to play for another season.
"His experience will prove vital for Scunthorpe next season, especially now they are in a higher division. He will be a great asset to the club.
"I am pleased he has chosen to join Scunthorpe. I will always have a soft spot for the club having played there myself. I hope he does well for them next season."