The 21-year-old has struggled for first team action at the Emirates Stadium since his arrival from Auxerre in 2013, and has just one competitive goal for the club - against Borussia Dortmund in the UEFA Champions League in November.
Bordeaux had been strongly linked with a temporary move for the striker, but Palace have won the race for his signature, making him Alan Pardew's first signing at Selhurst Park.
Palace's new boss is looking forward to seeing the France Under-21 international in action having admired his talent while with former club Newcastle United.
"He's a young player with tremendous promise, somebody that I have tracked personally and this club has too so that fitted well," he told Palace's official website.
"We have given him an opportunity, he needs to play more games and I think he's ready for that and he proved that at Arsenal.
"It's tough to get in their team but he's closer to the starting action with us."
Sanogo will go straight into the Palace squad for Saturday's crucial Premier League clash with fellow strugglers Burnley at Turf Moor.
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