Maybe a month.  Usually after they finish the background they will notify you of your Quantico date.  Your spouce, if you have one, is the last person they will talk with on the background.   If you completed your medical exam and you haven't heard anything on it, you can assume there isn't anything you need to clear up and all went well.  So generally about a month until you go to Quantico.  While in Quantico you will find out where you're first office will be located and you will be given time to search for housing, and when you find something you can start the process of selling your current place and moving your family.

Well I don't have anything crazy in my employment history nor my personal references so I think everything should go well.

About how long normally would I have after the background is complete to prepare my family for a Quantico departure????

Unless you have past employers stating that you were a bad employee, or references stating you're a shaddy character, you have nothing to worry about.  I passed, and I left two jobs with no notice given.  The FBI understands that those things are gonna happen.  It's BIG things that will fail you on the background.  By the way, expect the background to take about a month or so.  If you traveled out of the country often it could take up to 3 months.  Good luck.

I've passed every other stage in the application process and was told they have opened my background check.  I am still waiting on the results of my medical, but feel good about it.

My question what is likely hood of failing the background check???  Also if everything goes well, about how long would it be before I would be shipped to Quantico.   

I was told my background has been open for about a week.