Fox came through the ranks at The Valley, making 116 appearances, including 30 this season, and also spent part of the 2013-14 season on loan at Notts County,
The former Wales Under-21 international, whose signing was announced on the Owls’ official website, will provide competition for Daniel Pudil and makeshift left-back Adam Reach at Hillsborough.
He is cup-tied for Sunday’s FA Cup clash with Middlesbrough but should be in contention for this debut the following weekend when sixth-placed Wednesday host fellow play-off hopefuls Huddersfield.