UPDATE:
Sharing your podcast on Spotify gives you access to millions of Spotify listeners!
You can now easily submit and manage your podcast with Spotify for Podcasters. Just head there and request access (you’ll need an active Spotify account to log in with).
There's more info on this here.
----------------------------------------------------------------
Spotify should add a way for podcast hosts to submit/upload their podcasts to Spotify.
Currently Spotify has a list of aggregators to use to get music on Spotify, but there should also be a way to get your podcasts onto Spotify.
Updated on 2018-02-23
Hi all,
As @MattSuda has rightly pointed out, you can now go to this FAQ to learn more about getting Podcasts on Spotify.
If you have any further questions, you should reach out to the team directly using the 'Contact Us' section at the bottom of that site.
Thanks!