Final answer:
The Inca Empire was conquered by Francisco Pizarro, who used political turmoil and military might to overthrow the Incan ruler Atahualpa and claim Peru for Spain.
Step-by-step explanation:
The Inca Empire was conquered by Spanish conquistador Francisco Pizarro. He led an expedition to Peru after hearing of its riches, setting out in 1530 with the backing of Queen Isabella of Portugal and Emperor Charles V of Spain. Pizarro took advantage of a civil war within the Inca Empire and the recent death of the Inca ruler from smallpox. After capturing and executing the Inca leader Atahualpa, Pizarro established control over the Incan capital of Cuzco, securing the vast silver deposits and other riches of Peru for Spain.