The Gunners supporters were furious when Koscielny put up a video announcing his departure.
It was a video showing him removing the Gunners' kit and putting on a Bordeaux shirt.
Many fans, including legend Ian Wright, felt it was disrespectful.
"I had 9 incredible years there, lots of memories with this club," Kosc told a French outlet.
"I know that my announcement video at Bordeaux caused a bit of a stir, I want to apologise to the fans for that, I didn't expect it to affect them in the way that it did."