Sunday's 1-0 home defeat by rivals Bristol City left them 14th in the Championship and seven points adrift of the top six after 16 matches.
"Today I am leaving my beloved Bluebirds after over three years of which have been some of the best days in my long football career," Warnock said in a statement on Cardiff's official website.
"It is a shared belief that this is the right time for a new voice as we believe this squad of players is more than capable of getting success," Warnock continued.
"Finally, I would like to thank all you supporters for getting behind me and the team. I hope you have all enjoyed the journey. I am proud to leave the club as a united one and long may you all achieve the success that you deserve. Be lucky."