The announcement was made to the London Stock Exchange this morning and brings to an end a six year reign.
Ridsdale - under huge pressure from fans to quit after a poor season and mounting debts - will continue to serve as a non-executive director.
Professor John McKenzie, a board member, will take over as chairman.
Said Ridsdale: "This has been a very tough six months for the company and our performance both on and off the pitch has been unsatisfactory.
"This means that tough action has had to be taken to generate funds from player sales and to reduce costs both on and off the pitch.
"Although difficult it is necessary to balance our books to suit our current position.
"One outcome of this has been to subject me to significant comment, and created pressures that are not right for me, my family or the club."
The club confirmed losses had risen to £17.2m ($27.7m/EUR24.98m) for the six months up to December 31 - compared to £13.8m ($21.72m/EUR20.04m) the year before.
