How long does it take for v39 to roll out?
It has already started 2 days ago. As to the question when will it be fully implemented on the global scale in the live game, that would be when the game forces everyone to get the update. Here, have a read on this:
When do forced updates typically happen in the past from announcement of a new release?
About a week or so? There will be an announcement when they do server maintenance to disable the previous version.