The two clubs had earlier agreed an undisclosed fee for the striker and the 26-year-old has now completed the switch.
"This is a big step in the right direction for us," Holdsworth said in an official club statement.
"We've addressed our defensive and midfield situation and plenty of work has been undertaken to sign Craig to address the attacking area of our game.
"I must thank the club, chairman and Richard Low for having the same enthusiasm as me to ensure this deal has been completed. I know Craig well. He has an excellent professionalism, character and work-rate and he will rub off on the players. He's an excellent addition to our squad."
Reid will team up with Holdsworth for the second time after the pair worked together at Newport County, where the forward netted 58 goals in 96 matches.