City are believed to have paid The Hatters £75,000 for the striker's services, with another £50,000 to follow if Dave Jones' side win promotion.
Feeney joined Luton from Stockport in March 2005 for £175,000 but failed to make the desired impact in Bedfordshire, with his tally this season reading just four goals from 32 appearances.
The 26-year-old has escaped an entrenched relegation battle at Kenilworth Road and will instead be hoping to win Cardiff a place in the Championship play-offs.
Feeney is a current Northern Ireland international and joins up with his countrymen as they face Liechtenstein and Sweden in the coming week. He will then join his new team mates as City prepare to face Sunderland on Saturday week.