The French defender has been granted his wish to return to France following a nine-year spell at the Emirates Stadium.
The former club captain caused controversy last month when he refused to travel to the United States for Arsenal's pre-season tour.
Koscielny hoped that his decision would put pressure on the club to sell him in the final year of his contract.
And the 33-year-old looks to have got his way as Bordeaux close in on a £4.6m deal.
Unai Emery tried to persuade Koscielny to stay put for another campaign, but the former Lorient man was determined to return to Ligue 1.
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