Tobacco is native to the Americas and was domesticated in north America. Mesoamerican cultures, cultures in the US Southwest, and Mississippian cultures all used tobacco. I can't speak for the other areas, but in the Southwest it was smoked in pipes and possibly ingested through other means (perhaps directly). Large quantities of tobacco can be hallucinogenic or have other effects beyond just smoking a cigarette or out of a pipe, and it seems to have been related to religious rituals in some way or another. Casual consumption of tobacco wasn't really an activity in the Southwest.

Tobacco, and the method of smoking it (in pipes), was taken back to Europe by Europeans after contact. After that, I can't tell you when cigarettes were invented.