The Spanish side confirmed the signing of the Argentine, who has lived in Spain for three years, after spotting him during a trial.
"They only have to be a standout," said Real Madrid spokesman Juan Tapiador.
"We look for something different, that quality or talent that makes them stand out from the rest."
Coira begins training with the club's children's team in September and Real will pay for his travel costs, although he won't receive a wage.
"[My] dream is to meet [Lionel] Messi, play in the first division with Madrid and for Argentina in the World Cup," Coira told Spanish newspaper ABC.