Goal revealed earlier on Tuesday that an agreement to take the 33-year-old back to his homeland was in place.
That has now been pushed through, with the Gunners bidding farewell to a long-serving member of their playing staff.
Arsenal had been hoping to convince Koscielny that he should see out the remaining year on his contract in north London and aid their cause in 2019-20.
They have, however, bowed to the player’s wishes after it became apparent that he wanted out and Bordeaux were prepared to put a suitable off on the table.
A statement on the Gunners’ official website read: “The centre back has made 353 appearances for us since signing from Lorient in 2010. He was part of our Emirates FA Cup-winning squads in 2014, 2015 and 2017.
“Laurent, who started his career in the French second division at Guingamp in 2004, has played 51 matches for France and was entering the final year of his current contract with us. We decided to sanction his move to Bordeaux once we agreed acceptable transfer terms.
“We thank Laurent for his contribution to the club and wish him all the best for the future.
“The transfer is subject to the completion of regulatory processes.”
Koscielny finds himself back in French football for the first time in nine years.
Arsenal were able to get loyal service out of him, but his heart was set on heading home this summer.
He is now preparing to reacquaint himself with Ligue 1, a division he has previously spent just one season in.
His displays for Lorient in 2009-10 convinced Arsenal to make a move, with the man with 51 international caps to his name having spent much of his career in the French second tier prior to that.
Arsenal got full value out of the £8.45m they paid for Koscielny's services and have done well to recoup a large chunk of that fee when moving him on again.