The Scot has claimed in a statement through his lawyers that he has been "forced" to step down from his role at Ewood Park due to his position becoming "untenable".
"For reasons that I cannot discuss on legal advice, it is with deep regret, given my hard work and service for the club for a number of years, that I have been forced to resign as manager of Blackburn Rovers Football Club with immediate effect, due to my position as team manager becoming untenable," he said.
"I wish to thank all the players and coaching staff for their great support and the majority of the fans, who now see their club heading towards an automatic promotion position back to the Premiership. I wish the club all the very best for the future."
Kean's future at the Lancashire club had been in constant doubt since he was given the job in December 2010 following Sam Allardyce's departure.
Rovers were relegated from the Premier League last season but have won four of their opening seven matches in the Championship this campaign.
However, last Friday's defeat to Middlesbrough heaped more pressure on Kean.