One source of tobacco was Turkey and trade deals were concluded in the 1940s to supply tobacco as well as other commodities to Germany:

... the British were informed that Turkey had agreed to distribute German goods held in Turkish warehouses and to export approximately 5 million Turkish liras worth of Turkish goods including cotton, sesame seed, hazel nuts, tobacco, and most important .. olive oil.

On July 25,1940, as commercial agreement was finally signed ... The Turks were to supply Germany with a full variety of farm commodities, including mohair and olive oil.

A footnote to the statement above indicates that "Under the terms of this agreement, one-third of the commodities to be shipped to Germany from Turkey consisted of tobacco."

Source: Edward Weisband, Turkish Foreign Policy, 1943-1945.