The club's former chairman, who had held the role since May 2010, stepped down to embark on new career and business pursuits.
Lim, who will also continue his chief executive duties at the club, told the club's official website: "First and foremost, I would like to place on record my utmost respect to Dato' Chan Tien Ghee for his valued contribution to Cardiff City Football Club over the last three years.
"TG leaves a legacy that we can all be proud of and should all work hard to see continued.
"My ongoing remit is to work closely with the board and local management team over the final months of the season. With hard work and a collective mind-set from all connected to the club, God willing we will achieve our goals."
The Bluebirds are currently five points clear at the top of the Championship ahead of the clash with fifth-placed Leicester next Tuesday.