The Algerian defender got his move to the Premiership after Brian Laws claimed he 'begged' to leave to pursue his top-flight dream.
Although Bougherra's championship sabbatical could be over in May as Charlton are struggling in the relegation zone, their fate could be even harder with his first three games away at Bolton before facing Manchester United and Chelsea at The Valley.
Addicks boss Alan Pardew told his club's official website: "Madjid is a player who has come into English football and proved that his type of game can adjust.
"He has a real presence and power on the pitch that we hope to harness in our team, not only during the run-in this season but for years to come."
It is believed that Wednesday will have a sell-on clause for the player and that could net them extra cash, as well as appearance money and other clauses.
But Bougherra's departure could mean good news for academy product Mark Beevers, who could be called in for his debut on Wednesday at Southampton because of injuries to Richard Wood and Graham Coughlan.
Meanwhile it's good news for Marcus Tudgay - he became a dad to young Mason last week it was revealed today.