The transfer brings an end to a nine-year spell with the Gunners for the France international. During his time with Arsenal, Koscielny won two FA Cups, and he was named captain of the club following the retirement of Per Mertesacker in 2018.
Koscielny has long been a popular figure among Arsenal supporters, and they will likely be disappointed by the manner in which he departed the club.
The 33-year-old refused to travel on the team's pre-season tour to the United States as he sought to force a move away from the Emirates Stadium.
According to James Olley of the Evening Standard, the Frenchman made it clear to Arsenal he wanted to go back to France:
Mark Mann-Bryans of the Press Association said Koscielny was keen to be released on a free transfer:
Mark Mann-Bryans @MarkyMBryans
Understand Koscielny asked #AFC to be released from his contract this summer to join another club. Upon rejection of that request, he has refused to travel on pre-season tour and club will open disciplinary proceedings in the coming days. Losing captaincy almost certain.
Although his conduct will leave a bitter taste, the defender will be missed in north London next season.
While Koscielny's career has been blemished by a number of injury problems in recent years, he showed in 2018-19 that he can still be relied on. Although he lacks the dynamism he once had at his peak, the Frenchman is positionally astute and brought crucial leadership to the side.
It will be intriguing to see how he fares at Bordeaux, especially having spent so long at Arsenal. Given the controversial manner in which he left his former club, there will be an expectation on him to perform at his new side.