News of the recording by Kirk Ramsay – which was of discussions about controversial college sector reforms – was revealed at the weekend. Mr Russell then urged the chairman to consider his position.
Mr Ramsay said: "My resignation follows an unwarranted personal attack on me by Michael Russell.
"My passion and commitment for Stow College, and the college education sector as a whole, is too great for me to allow any perceived error on my part to be allowed to inflict damage on the college, its students or staff, executives and Board.
"I remain firm in my belief that I have done nothing wrong and intend to clear my name.
"I especially look forward to meeting the Parliament's Education Committee should they decide to launch a formal inquiry, which I sincerely hope they do."
A college statement said: "It is with great sadness the board has received the resignation of Kirk Ramsay. We accept that, in the circumstances, it is the honourable thing to do."
Mr Ramsay had distributed the recording to a small number of people directly involved in the implementation of college reforms.
Mr Russell suggested at a meeting with Mr Ramsay on Wednesday that he should consider his position.
But the Education Secretary came under fire in the Scottish Parliament yesterday when he was accused of trying to "bully and intimidate" college staff.
Labour education spokesman Hugh Henry said education staff had contacted him to say they were "frightened to speak out" against Mr Russell.
Mr Russell replied that most of his meetings with the college sector were positive and said Mr Ramsay was wrong to record their discussion.
He said he had no power to demand any individual's resignation because ministers' power of direction over the college sector was removed by the previous Labour-led Scottish Executive.
Mr Henry suggested it may be appropriate to record meetings for accuracy and argued it may be "in the public interest to publicise what the Cabinet Secretary said or how he behaves at meetings".
Mr Russell rejected the claim, arguing "the issue is that in a meeting of chairs and principals a recording was made with a surreptitious device. Nobody was told it was being recorded and no permission was sought from anybody who was present".
A Government spokesman said: "Mr Russell's position has been clear throughout. This has always been a matter for Mr Ramsay and the board of Stow College. We respect Mr Ramsay's decision."