Simply put, I got a job promotion the requires me to move to another city. I have spoken to my landlords about this subject and they tell me that there is a breaklease fee equal to 3 months rent and that it was located in my lease along with the other ways to break a lease... sublet. When I looked at my lease there was nothing in there about breaking a lease or any fees regarding this matter. Closest thing in there was at the completion of my lease if there is no written intent to vacate the lease will automatically renew for a 2 month period and a rate equal to each months rent plus $100 dollars for each of those two months. Am I entitled to pay the "break lease fee" if it is not mentioned anywhere but word of mouth?

If it's not in your lease then legally you're not required to pay all that, you didn't sign to agree. Although I would read everything very carefully before any actions are made, small print and all making sure you understand exactly everything that lease says. Congratulations on your promotion, and the best of luck!

If there is no clause, then you just can't break the lease, and they can hold you liable for the full amount of the lease.

This is normal, Actually them allowing you out with only paying 3 months is fairly nice.

In Fl for example they don't even have to try and rent your place, they can leave it empty and charge you rent to the end of the lease, in many places they are required to try and rent your place, and you will owe only to the point that they rent it.

Go back to the landlords and ask them to point out where in your lease you can find this clause. If you can't find it, then you are in a worse position, not a better one.

If there is no early termination clause then you are required to fulfill the terms of your lease. So, if they offer you a 3 month early termination charge, then you may be getting a bargain. However, if there is no clause in the lease you might try negotiating a better deal.