A royal ordinance of Louis Philippe I, King of the French, was issued 189 years ago, on 10 March 1831. That ordinance ordered the formation of a Foreign Legion with the aim of engaging foreign deserters asking to serve France and, too, foreign soldiers of then the freshly disbanded Hohenlohe Regiment (ex-Hohenlohe Legion or Royal Legion). Until the 2000s, the 10th of March 1831 had marked the official birthday of the current French Foreign Legion which derived its origin from that original 1831 Legion. Nevertheless, the lineage of the current Legion is far more complex. See a more detailed article.

Because of that, the official birthday was quietly changed in the last decade to the more neutral 9th March. To understand this step and to map the entire lineage of the current Foreign Legion, see this detailed article:
French Foreign Legion: The Lineage