How do I report buying out my brother's half of a previously shared rental income property?

You will add an asset to the Asset/Depreciation schedule for what you bought.

So your building will actually look like two places for depreciation as one has a basis for what it costs in the beginning and then the 2nd one will be the recent cost. 

What you will need to do, is first determine what you all bought and then allocate what you paid for it.  So for example if you paid $100K, then some will be the building, some will be land, some may be furnishing, some appliances, etc. until the $100K is all allocated.  then enter these assets in the Asset/Depreciation schedule for the rental.