The battalion, part of the joint Franco-German Brigade, is stationed at Illkirch-Graffenstaden outside Strasbourg, near the German border, and will by 2012 consist of 600 battle-ready soldiers.
The historic move, aimed at cementing friendship between the neighbours who fought three devastating wars in 75 years, was agreed by French President Nicolas Sarkozy and German Chancellor Angela Merkel at a Munich summit in 2009.
French Defence Minister Alain Juppe and his German counterpart Karl-Theodor zu Guttenberg attended a ceremony to mark the event, with Juppe hailing "a new impetus to move forward the construction of Europe."
Guttenberg stressed that "the cooperation between our two countries benefits all of Europe" as the 291st Infantry Battalion received its colours under a driving rain.
Merkel and Sarkozy, who held talks in the southwestern city of Freiburg on Friday, also hailed the troops' arrival.
"German soldiers are today welcome in France," Merkel told a joint press conference. "For me, that has great symbolism, after all the misdeeds Germany was guilty of during the Nazi era."
Sarkozy said: "It is an honour for us to receive German soldiers in a peaceful context on the French Republic's territory."
"I was always surprised that the Franco-German Brigade only consisted of French soldiers stationed in Germany. We are two sovereign nations, two countries at peace, two countries that founded Europe," he said, in apparent reference to the European Union's 1952 forerunner, the European Coal and Steel Community.
The community was set up in the wake of World War II with the explicit aim of making another conflict between France and Germany materially impossible by creating industrial interdependence.
German soldiers have been arriving at the base since April and took part in November 11 Armistice Day commemorations alongside their French counterparts for the first time.
Two French regiments within the Franco-German Brigade, which became operational in 1989 and consists of around 5,400 troops, are stationed in southwestern Germany, at Donaueschingen and Immendingen.
The German battalion is to be stationed in Alsace, a region that changed hands several times between France and Germany over the centuries.