Madine, who made eleven appearances whilst on loan at Coventry City last season, completed the move from Carlisle United for an undisclosed fee on Saturday.
Madine has signed a contract which will keep him at Hillsborough until 2015.
Carlisle managing director John Nixon has been reported as saying: "We have been in discussion with Sheffield Wednesday since Thursday about Gary, and the player was keen to make the move once he had spoken to them and to those who advise him.
"Our manager then spoke to him and, after some consideration, we reluctantly agreed that we would accept the offer and allow him to go.
"He feels that it is a big club, with crowds often in the region of 15-20,000, and moving to a club like that is a challenge that he wants to take