The first diffusion of the domesticated potato was within the Americas. It started (possibly thousands of years ago) when early farmers from the highlands of southern Peru, took their crop plants both further north into Central America and South to southern Chile.
The next major spread of the potato came as a result of the Spanish invasion of South America in the 1500s. An early account of the potato (published in 1551) by the Spanish explorer Cieza de Leon describes it as "… a kind of earth nut, which after it has been boiled, is as tender as a cooked chestnut, but it has no more skin than a truffle, and it grows under the earth in the same way."
It seems likely then that it was the Spanish that first exported the potato from South America. Though it appears that rather than being introduced directly to mainland Europe they were first cultivated in the Canary Islands. From there they were then shipped to European countries including Belgium and France. The first record of a potato on mainland Europe comes in the accounts of a Spanish hospital in 1573.
The cultivated potato was introduced to Bermuda by the British in 1613, from where it was introduced into North America in 1621. The British were then responsible for spreading the potato to India and China in the late 1600s.
Also in the late 1600s potatoes appeared in Africa and Japan and potatoes were introduced to New Zealand in 1769, being swiftly adopted by the Maoris who were already cultivating sweet potatoes ( Plant histories).
What do you think about this spread?