A former player and promotion-winning captain at the club, Yates returned to Whaddon Road in December 2009.
Yates led the team to the League Two play-offs in 2011-12 and 2012-13, but has paid the price for Cheltenham's poor recent run of form, which has seen them win just two and lose eight of their past 12 league fixtures.
Chairman Paul Baker released a statement on Monday expressing his concern at the results, and made reference to "underlying issues", without expanding further.
On Tuesday, Cheltenham confirmed that Yates had left the club, with an announcement on a new manager expected on Thursday.
"It was the most difficult decision I have had to make and the board has had to make in my time here," Baker said.
"It's a very sad day because Mark has done a huge amount for this football club and I would hate to think that people are going to think of his time here as the last 10 or 12 matches because his contribution to the club has been hugely significant.
"During his five years we've had some huge successes, but he also had to dig us out of a mess when he first arrived. That in itself, you could argue, was one of his best achievements. I have nothing but good words to say about Mark as a man and as someone who is passionate about this football club.
"That is why we originally brought him here because he understood the club and cared about it. Mark was understandably very upset and I was too. Everybody who knows him will have a lot of sadness with the decision we’ve had to take, but we to look after the business and look at results and performances.
"Something is not quite right and the manager has to take responsibility. He will be parting company from today and we wish him well in his future."
Cheltenham host Oxford United in League Two on Saturday.