The 63-year-old has ended his 15-year association with Donny amid reported tension regarding the takeover by Sequentia Capital.
Ryan was said to be angered when the rest of the board met with the Irish-led consortium, who he had originally identified to his colleagues.
"We can confirm that the club received a letter from John Ryan resigning as chairman of Doncaster Rovers," read a statement on the club's official website.
"Everyone at the club would like to thank John for the outstanding work he has done as chairman and for his hard work and efforts through the years.
"We hope he will remain a close friend of the club and continue to show his support for Doncaster Rovers. Everyone at the club continues to work hard with the same ambition and drive as usual in order to achieve our aims and objectives."
Ryan took over at Doncaster when the club was in the Conference in 1998.