Final answer:
The final battle of the Mexican-American War was the Battle of Chapultepec, leading to the signing of the Treaty of Guadalupe Hidalgo.
Step-by-step explanation:
The final battle of the Mexican-American War was the Battle of Chapultepec, which took place in September 1847. The outcome was a victory for the United States, which resulted in the capture of Mexico City. This pivotal battle paved the way for the end of the war and the signing of the Treaty of Guadalupe Hidalgo in February 1848, through which Mexico ceded large territories to the United States, including present-day California, Arizona, New Mexico, Texas, Utah, Nevada, Colorado, Wyoming, and Kansas, significantly expanding U.S. territory and fulfilling the concept of Manifest Destiny.