Minihan, who has signed a one-year deal, made more than 200 appearances for previous club Stockport and helped them to two promotions.
He joins other former Stockport players Jordan Keane, Harvey Gilmour, Matty Warburton, Jamie Stott, Milli Alli and Festus Arthur at The Shay, and Millington says it is an advantage that several of Minihan's new team-mates will be well known to him.
"We want to build a chemistry as quickly as we can and it's useful that he knows a number of the players already," Millington said.
"He's a real strong addition, fits into the group very well as a character, he's got a professional manner about him but he's also got a desire to be the very best he can be and to be successful, which shows in previous promotions.
"If you look across the make-up of the group, we've now got a number of players who, in the last 12 months, have experienced play-offs campaigns, promotion as champions and promotion via the play-offs.
"So we've got a group of players who know what it takes to get promoted from this level."