The 27-year-old joins the Bluebirds on a three-and-a-half-year deal and is rumoured to have cost up to £6m to prise away from relegation-threatened Bolton.
Madine was one of three options on the table for Cardiff, along with Bournemouth's Lewis Grabban and Ipswich Town ace David McGoldrick, the former of whom is now likely to make a temporary switch to Aston Villa.
City boss Neil Warnock has seemingly spent big to bolster his squad for their bid to reach the Premier League, though, with Wanderers recently declaring that they would not sell their star man unless a large bid was received.
After making his third signing of the winter window, Warnock told his side's official website: "He's been my number one choice all season and I'm delighted to capture him.
"He's been worth the wait, although I must admit that it wasn't until the last 24 hours that I thought it might be possible. I must thank Vincent [Tan], Mehmet [Dalman] and Ken [Choo] for their hard work in getting this over the line. I'm sure the fans will join me in welcoming Gary to the club."