The origin and domestication of sweet potato is thought to be in either Central America or South America. In Central America, sweet potatoes were domesticated at least 5,000 years ago. In South America, Peruvian sweet potato remnants dating as far back as 8000 BC have been found.

One author postulated that the origin of I. batatas was between the Yucatán Peninsula of Mexico and the mouth of the Orinoco River in Venezuela. The cultigen had most likely been spread by local people to the Caribbean and South America by 2500 BC. Strong supporting evidence was provided that the geographical zone postulated by Austin is the primary center of diversity. The much lower molecular diversity found in Peru–Ecuador suggests this region should be considered as a secondary center of sweet potato diversity.

The sweet potato was grown in Polynesia before western exploration. Sweet potato has been radiocarbon-dated in the Cook Islands to 1000 AD, and current thinking is that it was brought to central Polynesia around 700 AD, possibly by Polynesians who had traveled to South America and back, and spread across Polynesia to Hawaii and New Zealand from there. It is possible, however, that South Americans brought it to the Pacific, although this is unlikely as it was the Polynesians, and not the native South Americans, who had a strong maritime tradition. The theory that the plant could spread by floating seeds across the ocean is not supported by evidence. Another point is that the sweet potato in Polynesia is the cultivated Ipomoea batatas, which is generally spread by vine cuttings and not by seeds.