From the time I first applied online to the VERY first day I worked, it took approximately six months. There are a few steps in the process (please note that this applies to me only...as I have read in other reviews, some locations require a 'sort orientation').
1) Filled out an online application.
2) Filled out extensive paper-work, in-person, at a local recruitment center.
3) Interviewed with two FedEx managers.
4) Submitted paperwork for a background check and completed a drug test.
5) Attended an orientation session at FedEx.
6) First day of employment!
As stated above, the entire process took approximately six months. If you apply and don't hear back from someone for a few weeks (or months, as was my experience) don't get discouraged!