The short answer is ......... yes, just replace the lamps with 12v LED ones.
LED lamps do need a modern electronic transformer (driver) to operate properly. You may be lucky, and they will be Ok. It all depends on the transformer you have already.
They'll light up alright, but may flicker. That would be a sure sign that the transformer would have to be replaced. Even if you put up with the flickering, it would reduce the life of the lamps greatly.