The striker, signed from Evo-Stik Northern Premier side Grantham, will join Gozie Ugwu in the Spireites’ attacking options ahead of the National League season.
And Allen, who has handed trials to forwards Liam McAlinden, Gerry McDonagh and Lewis Walker in the past week, wants to add another to his front line.
“We’re hoping to be able to get in another centre forward which will allow us to have three centre forwards for two positions,” he said.
“Zavon (Hines) can play up there as well, but if we could have three out and out centre forwards then we will pick the best two to play.”
Shaw. 24, represents a change of tack for Allen and Chesterfield in their hunt for goalscorers.
He hit the net 33 times last season, having scored 28 in the previous campaign for Grantham.
“Carl Muggleton has had him on his list for a good month or so,” said Allen.
“It’s been well documented we’ve tried for players from higher levels, experienced players to come down.
“And then I kind of got to the point where I was thinking, do I want a seen-it-done-it player or a hungry, can’t-wait-for-it-love-it player?
“I thought with that attitude we would have a much better chance of being successful.
“His goalscoring record over the last three years, he’s got better and better as a player.
“I know lots of people in non-league up in this area and I’ve had rave reviews.”
Shaw was a wanted man this summer and spent two weeks training with Lincoln City, who Allen says made the forward an offer.
“Lincoln have offered him a contract but I think I got in at the right time on Sunday morning at 8.30am,” said the boss.
“We were on the phone for about 20 minutes, no negotiating, he said yes straight away. I spoke to his agent and he said yes straight away.”
Allen was impressed by Shaw’s determination to quit his day job the right way on Monday, preferring not to do it by text.
“He did tell me he had to go into the factory on Monday morning, he wanted to see his boss face-to-face and I like that kind of character.
“Having sat for an hour with him, he’s like a little boy waking up on Christmas day.
“When we were giving him his training tops and his gear he was like a little kid.
“He can’t believe the X-Factor change in his life.
“I hope all Chesterfield supporters get behind him now.
“We’ve got to hope he kicks on, he’s a buzz of a player, he doesn’t stop running, chases everything down and he’s the kind of player the paying public will like.
“He’s right up my street, I’m delighted we’ve got him.”