It varies. Depends on the branch of service, servicemember's rate, and how desperately a position needs to be filled. We've found out anwhere from 9 months to 3 weeks (current one was a week an a half in regards to the transfer date, not duty station - wasn't happy about it OR prepared sice it was originally 3 months down the line).
My advice: Don't be surprised by anything.
Good luck and hope it goes as smoothly as possible.