I don't see why fitting a tapered tube to a non-tapered outer tube is really much more difficult than joining two non-tapered tubes, using fibreglass belts, as Jami has already done. The two belts will be slightly different in thickness, but both will have the same outer diameter (to match the inside diameter of the outer tube.)

[If you want to make PERFECT fit (probably not necessary) you can reverse the smaller diameter tube and run it completely inside the outer tube, with a soft collar at the top end to maintain perfect concentricity - and use the inside of the outer tube, at the other end, as a casting mould for the fibreglass and thickened epoxy. Of course, you need a pretty good parting agent and a certain amount of courage! I have done this, but not sure if I would do it again. I used a parting agent – and two layers of baking paper to be on the safe side – and it was still a little difficult to part the two, and a matter of some relief when, with some work with a heavy hammer against a block of wood, the perfect inner did finally slide out - and then with the paper removed, reversed back in perfectly.]
A cone-shaped external fairing can then be added, to smooth the transition between the two tubes.

The glue joint just needs to be sufficient to withstand the downward pressure of the halyard and sail bundle, and also the rotating force which the halyard and yard will induce on the top tube. I have used epoxy glue, but believe that one of the flexible polyurethane rubber glues might be better practice. The "bury" should, of course, be minimum 10% of the upper part and its easy to make it a bit more. That conical external fairing of glass and thickened epoxy should take care of most of the downward and rotational forces, and just a few dabs of glue should be all that is necessary on the inside - think of it structurally as a tabernacle.
A more interesting question is joining two tubes when the outer tube is tapered.

This has been in the back of my mind for over a year now, since I acquired a couple of large spinnaker poles from Marcus, who got them off one of the Volvo round-the-world yachts that must have called in to Whangarei some years ago. These are top quality heavy wall aluminium tube, tapered at both ends.

One of these spinnaker poles will make an excellent bottom section for a mast I have in mind. (I should explain, despite having an aluminium smelter, we can't get tapered aluminium poles here in New Zealand, and only a limited range of parallel tubes.).
It does seem a pity to cut off the tapered parts. (A taper at the heel would be an elegant feature, and the taper at the top of the mast base would lead nicely to the diameter of the next tube.)
It’s just a matter of how to do it.
Howard has scoped the problem correctly, and David has provided good advice on similar questions in the past - a castable material which can be poured into the annular cavity, and a dam at the end of the cavity to contain the material until it sets, and to keep the two tubes concentric. Now the interesting question is, just how to actually go about doing it: how to pour into the space between two concentric tubes with the outer one tapered down to match the approximate diameter of the inner one. A nicely fitting stiff foam or rubber flange on the end of the inner tube might be sufficient as a dam. Now, how to pour in that castable material? Turn the mast upside down, vertical, and work from an upper balcony? In that case, you wouldn’t need the dam.
And now the real challenge - how to get a poured join between two concentric tubes when the outer one is tapered at both ends!

So far I can think of only one way and that is to lie the two tubes horizontal, supported firmly so as to maintain concentricity - and pour through a hole in the side of the outer tube. I still haven't figured out how to get a dam in there!
I bet there is an answer though. A balloon?
Some lateral-thinking mechanic will come up with a way, those fancy spinnaker poles are too good to send to the scrap yard.
PS I am not so sure about Howard's suggested detail of a flange welded to the mast at the point where it goes through the deck. The "Spartite" detail would seem to be not only sufficient, but simpler and possibly better.