
The 24-year-old striker has agreed a three-and-a-half year contract with a two year option and is eligible to play in Saturday's home game against Chelsea.
McFadden, whose price could rise to 6 million pounds depending on appearances, becomes manager Alex McLeish's second signing since the opening of the January transfer window, following the acquisition of full back David Murphy from Hibernian.
Former Scotland manager McLeish's decision to step in for the player was no doubt influenced by McFadden's excellent scoring record for his country of 13 goals in 37 appearances.
DPA