In a statement, police said Antoine Denevi, a 27-year-old originally from the northern French region of Pas-de-Calais, was detained on Tuesday in the southern Spanish area of Malaga at the request of French authorities.
He reportedly moved to Spain using false papers shortly after the attacks in January 2015.
Spain's El Mundo reported that the suspect was arrested in Rincón de la Victoria in Malaga on Tuesday.
Tributes to those killed in an attack on a Jewish supermarket in January 2015. Photo: AFP
The suspect "left the neighbouring country (France) weeks after the Paris attacks to escape police action, and settled in the province of Malaga from where he continued his illegal activities using fake papers," the police said in a statement released Wednesday.
"It's also been determined that his activities were linked with people of Serbian origin, who may have facilitated his access to arms and munitions."
Both Spanish and French police forces participated in Tuesday's operation, during which two other people were detained - one Serb and another from Montenegro.
Coulibaly was one of three Islamic extremists who waged attacks in Paris on January 7-9th last year that left 17 dead.
He shot dead a policewoman and later took hostages in a Jewish supermarket, where he killed four people.
His accomplices, the Kouachi brothers, killed 12 in an attack on the office of satirical magazine Charlie Hebdo.