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The U.S. made a deal with Mexico and as a part of that treaty it acquired a certain portion of Mexico's land which is now the American Southwest.
Initially, the Mexican government resisted peace talks despite the defeat in the Mexican War. The US military actively controlled Mexico City, the capital city. The currently occupied Mexican government was forced to negotiate because it did not have a strong bargaining position. Their goal was to maintain power. So the United States did what they wanted and the the deal was the Treaty of Guadalupe-Hidalgo.
The 1848 Treaty of Guadalu Peidalgo defined most of the southern border of the US mainland, including the part along the Rio Grande River. As a result of the treaty, Mexico had to give up all of this land. The U.S. paid them $15 million plus $3.5 million in debt relief.
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