On January 2 , 1492 , the last Muslim leader , Muhammad XII , surrendered complete control of Granada , to Ferdinand and Isabella , after the city was besieged . On January 2 , 1492 , the last Muslim leader , Muhammad XII , known as Boabdil to the Spanish , surrendered complete control of Granada , to Ferdinand and Isabella , Los Reyes CatÃ licos ( `` The Catholic Monarchs '' ) , after the city was besieged .