Lim, who replaced Alan Whiteley as chief executive in 2012 and briefly took over as acting chairman from Dato Chan Tien Ghee the following year, oversaw Cardiff's promotion to the Premier League.
However, following an immediate return to the Championship, Lim has ended his association with the club, with chairman Mehmet Dalman assuming his responsibilities.
Cardiff also have appointed Ken Choo to the role of general manager.
Lim said in a statement on the club's official website: "It's with great pride that I held the office at Cardiff City, but feel now is the right time to move on, allowing the club time to make adjustments over the summer before another important season.
"I'm honoured to have represented the club during our historic promotion winning year and very much hope to once again see Cardiff City in the Premier League at the earliest opportunity.
"I am indebted to Tan Sri Vincent Tan and the board for giving me the opportunity and would like to thank the hard-working and dedicated staff at the club for supporting me during my time in south Wales.
"I wish them and all associated with the club every future success."
