First off, the end of a round leg isn't always tapered. Instead some are just round tenons, which are usually (but I don't think always) then wedged.
The idea behind a tapered tenon in chairmaking is that it helps prevent the leg working loose over time – remember, they used to build for the ages – as it's always trying to work its way tighter into the tapered fit of the hole if the wood compresses over the years as pressure is put on the seat. A wedged tenon seeks to achieve the same end by another means, by compressing the wood at the end so well it just can't work loose over time1.
Anyway, to make a tapered hole the usual tool to do this is a reamer of some sort, which is used after a straight hole is drilled to turn it into a tapered hole. Chairmakers often made their own reamers in the past, and some still do, but they are made commercially. There isn't just one way to do the corresponding part on a leg, it can be formed freehand by drawbore/spokeshave work, even using a rasp or file or just by sanding. But there are commercial and user-made tools for forming these accurately and repeatedly, and to reduce the drudgery. Now you know the end of a leg is a type of tenon it makes it easy to find one type of tool for this work, they're simply called tapered round tenon cutters. These commercial tools are matched to work as pairs since obviously they need to have the same taper and work with the same diameter(s).
I think you should try a basic round tenon first though. Apart from wedged through-tenons being a potential plus on the looks front (using wedges of a contrasting wood), there's another reason to prefer these — you don't need to buy any specialist tools. You can form the round tenon by numerous means using existing or non-specialist tools, and the simple round holes of course only need a suitable size of drill bit2 to chuck into your power drill or brace.
1 Along with the glue naturally, although you can wedge a tenon and use no glue and end up with a very strong and long-lasting construction.
2 Usually an auger or flat bit/spade bit would be used.