How to leave PhD program without causing problems
I want to leave with a master's degree and move on with my life.
  I don't know how to explain this to my department.


Directly, as though the department chair were an actual reasonable human being and not a soul-sucking tentacled horror from the nether dimensions.


  I fear they will try and force me to leave without a master's degree even though I have met the requirements.


I would suggest starting by finding out the mechanics of getting the master's degree.  Perhaps if you do nothing, the degree will magically appear in your academic record, but more likely there is some paperwork that you have to fill out.  Find out what that paperwork is.  Fill it out.  Collect the necessary signatures, and submit the completed paperwork to the relevant campus office.

You don't have to tell them why you want the master's degree. In my experience, it's quite common for PhD students to pick up a master's degree along the way to their PhD, either as a backup if the PhD falls through, or as a boost on their resume when they look for summer internships / employment.  Once the master's degree paperwork is done, inform the department that you will not be returning next term.  Finish your classes, look for jobs, and move on.

But at a more fundamental level, you really don't have to defend your decision to leave.  You did not promise to complete the degree program.  You did not sign a contract.  You are not an indentured servant.  You do not "owe" the department.  Your departure will do  the department no permanent damage.  Yes, a few people may be disappointed by your departure, but they'll get over it.


  I have never heard of someone quitting after passing the qualifying exams


For what it's worth, I left my first PhD program with a master's degree after passing my qualifying exams.  (Admittedly the circumstances were different — I left to join a different PhD program — but I was far from the only person in that department to leave after passing quals.)