Webers are generally not convertible from propane to natural gas and vice versa. If you were previously using a propane tank, then what SMS said... just swap the regulator... works fine. But, you cannot simply run a natural gas appliance on propane or vice versa without a orifice conversion... propane is about 2500 BTU per cubic foot, natural gas about 1000.
There are two types of regulators that fit the different brands... Esso and Mobilegas, I think. They are not interchangeable so decide whose going to be your local dealer and talk to that one about getting the regulator. Maybe the regulator price is a factor. Both regulators output the same pressure but one of them has a slightly higher CFM rating... probably doesn't matter for a BBQ, did matter when deep frying turkeys as it took longer to heat the oil.
If you have previously been hooked to a natural gas line, then you will need to do the same here IF the
property had it installed years ago... many properties did not... my first semi-D had city gas, the second did not.