Carlo Ancelotti has turned down the chance to return to AC Milan, telling the club he needs rest.
Jose Mourinho insists Diego Costa is content at Chelsea in response to reports linking him with a return to Atletico Madrid.
The 32-year-old will stay at Hillsborough for 28 days and follows Manchester City defender Jeremy Helan, who arrived on loan earlier today, into the club.
Sidibe first arrived in England when he joined Swansea in 2001, scoring seven goals in 26 league starts before moving on to Gillingham.
He joined Stoke on a free transfer in the summer of 2005 and has scored 26 goals for the Potters in 186 appearances.
Sidibe will go straight into the Owls' squad for this weekend's home game with Leicester.