Sweet taters hail from Central or South America and date back thousands of years. Fairy early on, they went to the Caribbean(1,2) and American Southeast. Islands in the South Pacific are believed to have acquired them after about 1200 AD(2), [which would have coincided with the last of the Crusades and part of the occupation of the cliff dwellings in the American Southwest.]
A lot of scientists think that the South Pacific Islands got colonized from Asia on an easterly course. The Norwegian mariner Thor Heyerdahl, though, who sailed a native-materials balsa log raft from Peru to French Polynesia in a 101-day, 4,300-nautical-mile voyage, believed that the presence of sweet potatoes and Inca legends point to South American colonization of the South Pacific(2). [I read his KON-TIKI, which told about those couple evidences and architectural similarities. His presentation of facts seems to make much more sense to me.]
Christopher Columbus was among the initial European samplers of the tasty tubers and liked them enough to take them back with him on his last, fourth voyage to the Americas(1,2). Warmer parts of Europe would catch on to them afterward(1). Hernando de Soto also encountered them on his 1500s joggle through the American Southeast; they were an early-on staple of the Southern colonies(2). Exportation of sweet potatoes to China would happen by the late 1500s; they reached further to "Asia, Africa, and [more of] Latin America during the 17th and 18th centuries."(1)
Sources:
1. Admin. "Interesting facts about sweet potatoes." Just Fun Facts. JustFunFacts.com. Web. 21 Dec. 2020. http://justfunfacts.com/interesting-facts-about-sweet-potatoes/.
2. Fuder, Josh. "Sweet potatoes are more than just a side dish." University of Georgia College College of Agricultural & Environmental Sciences. University of Georgia, Athens, GA. 7 Dec. 2019. Web. 21 Dec. 2020. https://grains.caes.uga.edu/news/story.html?storyid=8208&story=Sweet-Potato-History.