The Englishman had been on loan at Hillsborough, but has now signed a three-and-a-half year deal after Wednesday agreed an undisclosed fee with Norwich.
Hooper joined the Owls on loan in October and scored six goals in 12 Championship appearances.
The 27-year-old leaves Norwich after two-and-a-half years with the club following a move from Celtic. He scored 20 goals in 70 appearances for the Canaries.
