What to Do When Love Blossoms in the Office
Research suggests that half of all relationships start at work. If you're a manager, the question is not whether you should allow it to happen, but how you can ensure that it doesn't have an adverse impact on your organization.
It would be helpful to introduce a policy addressing relationships at work and setting out what behavior is unacceptable, what is permitted and when, issues about conflicts of interest and, probably most importantly, what to do about the very common situation in which the boss is in a relationship with a subordinate.
Be sure your policy does not distinguish between different types of relationship - you are not a moral policeman. So whether it's two young things in the first flush of love or a married person using the pool of available talent for some excitement on the side, the same rules apply. And remember that it would be illegal to treat gay relationships any differently.
You are right to be concerned about the impact on the workplace - not just if they fall out, but while they are continuing the relationship. They come to work to work - it's not a convenient lovers' meeting place.
At least they have been open enough to let you know about the relationship (and if they haven't, you have every right to challenge them discreetly about it). So right from the start, lay down some ground rules.