The 27-year-old moved to the City Ground on loan at the end of November with a view to making a permanent switch in the new year and he has now signed a two-and-a-half year contract.
Tudgay has been an instant hit with the Forest fans, scoring three goals in as many starts.
He started his career at Derby and scored 18 goals in 99 appearances for the Rams.
He joined Sheffield Wednesday in January 2006, scoring 50 times in just over 200 outings for the Owls, and was their top scorer last season.
Source: PA
Source: PA