The Caribbean island that became a U.S. territory after the Spanish-American War was Puerto Rico.
Puerto Rico was still a Spanish possession when the war began in 1898. U.S. forces invaded the island in July, landing at Guánica on July 25 and advancing against Spanish positions. An armistice halted the campaign before the Americans captured San Juan, but Spain agreed to surrender its claim to Puerto Rico.
The Treaty of Paris, signed on December 10, 1898, transferred Puerto Rico to the United States along with Guam and the Philippines. Unlike Cuba, which the treaty set on a path toward independence, Puerto Rico remained under American sovereignty. The United States initially governed it through a military administration and later established a civilian government.
Puerto Rico became an unincorporated U.S. territory under the Foraker Act of 1900. Congress granted U.S. citizenship to Puerto Ricans through the Jones-Shafroth Act in 1917. Puerto Rico is still a U.S. territory, not a state and not an independent country.