The Treaty of Guadalupe Hidalgo

The Mexican-American war was coming to an end, and the American troops had conquered Mexico City, forcing the Mexican empire to give up the war. As a result, the U.S., while also paying the Mexican government 10 million dollars, had made the Mexican government sign the Treaty of Guadalupe Hidalgo, which would ultimately give the California and New Mexico territory to the U.S. government, expanding the U.S.' territory by a third. 

Before the war, the U.S. government had offered the Mexican government 15 million dollars for the California and New Mexico territories, although the Mexican government had denied. With the annexation of Texas into the U.S. in 1845, tensions grew. The Mexican-American war had begun after conflict broke out on disputed Texan territory, Polk had declared war. Both governments could not agree where the Texan borders were, and as a result, President Polk sent his troops into the disputed territory where the Mexican military would shoot them down, officially starting the war between both countries. The war began in 1846, and the hopes of many Americans of expanding westward were happening, the American philosophy of Manifest Destiny called for the westward expansion of American culture and people, to connect the country to both sides of the continent. Though many Americans were beginning to spread and travel west in hopes of a better life and luck, many were already in northern Mexican territory, which helped the American cause of going into Mexico and taking more land. As was promised, the American people were destined to rule the continent, though popularity. 

Map illustrating the course of the war.

The Treaty of Guadalupe Hidalgo was finally signed on February 2, 1848, following the end of the Mexican-American war, adding 525,000 square miles of land to the American map. 

Sources:

http://www.history.com/topics/treaty-of-guadalupe-hidalgo

http://www.pbs.org/kera/usmexicanwar/aftermath/war_esp.html