In a statement issued through his lawyers, Kean said: "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.
"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 has been a much-derided figure at Ewood Park for the duration of his near two-year spell in charge, with the low point being relegation from the Premier League in May.
But despite poor results on the pitch, Kean retained the backing of the club's owners, Venky's - much to the fury of supporters who regularly protested against him.
The tide seemed to have turned for the 44-year-old this season, on the pitch at least, as Blackburn made a positive start to the campaign, with Rovers sitting third in the Championship table ahead of Saturday's trip to Charlton.
There was no sign of Kean's decision to step down on the club's website, with the lead story one of him talking of a "positive week".
Managing director Derek Shaw said: "I have been travelling down to London and this is the first I have heard of it."