Halifax-born Ridehalgh, who has signed a two-year deal, arrives after eight seasons at Tranmere Rovers, where he enjoyed two promotion campaigns.
Ridehalgh, 30, started his career at City’s neighbours Huddersfield and has also had loan spells at Rotherham United, Swindon and Chesterfield.
Ridehalgh said: “I played against a Derek Adams team in the play-offs last season. His sides are hard working and strong mentally, so I know what is expected.
“We are in League Two at the moment, but I know our aim is to go farther than this division.
“It is clearly an ambitious club. The new manager has come in and has past experience of getting promoted from this league. I think this is a Championship club so, hopefully, this year we can be right up there in the league.”
Meanwhile, former Doncaster Rovers captain Tommy Rowe has made his return to the club, signing a two-year deal after his release from Bristol City.
Rowe, 32, who has become the club’s fourth close-season arrival, said: “As soon as I got the interest from Doncaster, something felt right about it.
“I made my intentions clear that a move back is something that we were trying to push through and things progressed really well.
“I’m a firm believer that you play your best football when you’re happy and you’re enjoying it and that was present for my three years here. This is my second spell here and familiarity will help me but, ultimately, I’m ambitious and hungry to go again. I won’t settle at League One.”
Rovers and Doncaster Rovers will face each other in the group stages of the Papa John’s Trophy, with the full round-one draw to be completed this afternoon.
Sixteen invited Under-21 teams, including Leeds United, will be placed into their respective northern and southern section groups, with the 48 EFL clubs placed into pre-determined groups.
The Millers and Rovers will be placed in Group E alongside Scunthorpe United.
Bradford City will compete in Group F alongside Lincoln City and Sunderland, while Sheffield Wednesday and Harrogate Town have been pitted together in Group H with Mansfield Town.