Taylor told the Hull Daily Mail: "Without doubt, Andy is one of the best left-backs in the third division and I think he can also play in the next two as well.
"He's a very good attacking left full-back and he scored four goals last year. He's an excellent footballer and I'm really pleased to get him."
Dawson accepted a move to the Mudrats after a year spent at Scunthorpe on a weekly deal after turning down a three year offer last summer.