Question How did New Mexico become a U.S. territory? Responses Americans living in New Mexico started a movement and persuaded the governor to join the U.S. Americans living in New Mexico started a movement and persuaded the governor to join the U.S. A U.S. Army colonel and his troops arrived in Santa Fe and captured it without a fight. A U.S. Army colonel and his troops arrived in Santa Fe and captured it without a fight. New Mexico was part of the territory included in the Louisiana Purchase. New Mexico was part of the territory included in the Louisiana Purchase. Mexico gave New Mexico to the U.S. to avoid conflict with the Native Americans