Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Chelsea striker Fernando Torres is understood to be set for a return to Atletico Madrid, according to Sky sources.
The deal is set to run until January 1, but Norwich have the right to recall the player after 28 days.
With the loan window set to slam shut on Thursday, Cardiff have moved quickly to put an agreement in place.
Lappin, who will be free to take in a New Year fixture with Birmingham, will join up with the Bluebirds ahead of their weekend clash with Barnsley.
The 29-year-old will help to bring added competition for places to the Cardiff squad, as they attempt to steer a course to the Premier League.
Lappin, who has spent the last five years at Carrow Road, has been allowed to move on by Norwich after making just one Capital One Cup appearance for the club this season.
"An adaptable player, Simon can play as a left-back or in midfield," Cardiff said in a statement released on their official website.
"With defensive injury concerns this week, he is a welcome addition to the squad, while we would also like to thank Chris Hughton and Norwich City for allowing Simon to join us for this period."