You fell in love at work and because there is a company policy prohibiting dating your co-workers you need to find out how to keep secrets in dating them. This can be a tricky thing to accomplish, you will have to be very discreet. Obviously, you should be discreet anyway, after all, you are at work, not out at a club, but it can be even more challenging dating a co-worker because if someone finds out your jobs are on the line.
Your job is your livelihood and you can't afford to lose it. Maybe if this gets so serious one of you could go to a rival company or find different employment all together. Then the job thing would not even come into play.
One of the first things is to make sure you set the rules. You could try to pretend that you barely know each other at work and do not look or speak to each other all day. This could pose quite the challenge. But just think of all the laughs you could have when your day is done and you are home relaxing.
Your best bet is to not tell anyone anything, keep secrets in dating. If you choose to tell someone and then they get mad at you they will have the perfect ammunition to ambush you with to your boss. I don't care if the two of you have been friends since kindergarten, keep this a secret until you know where the relationship is going and if it is serious.
Stay professional at work at all times. Do not try to sneak off to the supply closet or send lovey-dovey emails on company time. Sometimes bosses have a program installed on their computer network in the office to track what their employees are doing on the computer on their time. If your boss has one of these programs he will see that there is a budding romance and then nip it in the bud before it has a chance to blossom.
Act like you are good friends, sit together at lunch and talk about everything and anything. Your co-workers may think they know something but if you continue to act professional and deny your involvement then the rumors will die down eventually. Someone may pick up on something but if you play it right and are extremely discreet, you will keep yourselves out of trouble.
Sometimes the stress of this type of situation can be overwhelming. This relationship may not be one that lasts because of the level of stress. Figure out what you both will say if someone does take a wild guess and accuses you of having an office romance. Keep your stories straight but maybe say things differently so you both are not giving the exact same answer. This is a dead giveaway.
If you keep secrets in dating and the relationship still does not make it then have a little class at work and do not do anything petty, accept that it was a mutual split and respect each other enough to not throw a fit.