Koscielny touched base in the French city on Monday, after positive talks between the two clubs in London a week ago.
The 33-year-old was hopeful that Arsenal would find a final agreement with Bordeaux to give him a chance to come back to France.
What’s more, the agreement was settled late on Monday.
Koscielny will have a medical on Tuesday, before penning a three-year contract.
The transfer fee is ought to be around €5 million altogether.
The Frenchman had dropped out with the English club during the summer for a reason unknown and would not go on visit in the United States with the remainder of the squad.
Koscielny joined Arsenal from Lorient in the summer of 2010 for €10m and proceeded to show up for the Gunners and to win three FA Cups.