If you do not want to setup a formal policy, then I would suggest addressing it via work performance issues. You state that it is starting to affect the one's work. To me, this is the perfect time to give a gentle warning about the company's expectations (such as keeping it out of the office, not during work hours, not affecting other employees, not discussing the relationship during work hours with other employees etc). If it is a supervisor/subordinate relationship, then I would strongly suggest giving one of them the chance to transfer.
You might also check to see what state laws your state has about an employees' right to privacy for behavior outside of work and fraternization policies. Some states are more employee friendly on this than others.
I have heard of companies who have both employees sign a document regarding the relationship, but it has been a while since I have seen one. And I have never needed one.