This interesting article uses the arguments of language taxonomy to suggest tobacco was actually brought to the New World by ancient African traders.
"The British introduced the Luo to cigarette smoking only a century ago. So how is it that the Luo have an indigenous word for a 'cigarette', ndawa? And why is ndawa – a 'Nilotic' word – so closely related to Kiswahili dawa and other Bantu words to do with healing?
Let us approach the question from another direction. Our President is called Kibaki. This is a native Kikuyu name. Yet there is something universal about it. Without the prefix ki (which denotes largeness), we get baki.
This is very close to the Luo mbaki and both are very close to the English baccy. The question is: Is the word kibaki etymologically related to the words tobacco (English), tumbaku (Hindi) and their cognates in other Indo-European languages? "
"The emerging evidence is that the plant and its name are totally native to Africa. It was the Africans who took it to both the Americas and Europe – and even Asia – and they did it millennia before the "Age of Discovery".