For some reason embedded links not working today. Hope the link above is clickable.
The history that I learned before is that Aztecs and Mayans domesticated turkeys. They were taken to Europe by Spanish explorers/colonizers/conquerors. From Spain they spread around Europe, but for some reason Turkish farmers did an especially good job selecting faster growing turkeys. Then they were exported, so the English called them Turkey Birds. Then on colonizing New England, they took them there.
So the Turkey, while a new world bird, came to N. America via a pan-European path.
That's the story I heard, but the linked article is more complicated. Fun to read, for me at least.
If the linking capacity comes back I'll edit this or add comments.