The 31-year old was a free agent after his contract with Burnley expired at the end of last season.
The winger made 39 appearances and scored two goals for the Clarets in all competitions last season.
However, he rejected the one-year extension handed to him by Burnley.
Welcome to Hillsborough George! #swfcpic.twitter.com/eXLbQwGNTV
— Sheffield Wednesday (@swfc) July 3, 2017