The move has long been rumoured all summer, which accelerated when the Frenchman reportedly refused to travel with the Gunners for their pre-season tour.
Earlier in July, Arsenal stunned supporters by stating they were ‘very disappointed’ with Koscielny for ignoring their ‘clear instructions’ to join the squad in the United States this week.
The centre-half joined the club in 2010, winning three FA Cups with the club in that time and making 353 appearances.
“We decided to sanction his move to Bordeaux once we agreed acceptable transfer terms,” read an official Arsenal club statement.
“We thank Laurent for his contribution to the club and wish him all the best for the future.”