It's not Spotify that's adding the music, it's record companies and labels for those record companies that upload songs and become Spotify artists. Basically, it's a bunch of 3rd parties that are partnered with Spotify to upload songs and get payed for uploading the songs.
@zachbeard's pretty much hit the nail on the head, there. To make sure everything on Spotify is properly licensed, we require all music to be delivered by labels and distributors. We have deals with most labels and distributors, so that's where the tunes come from.
If you're an artist looking to add your music to Spotify (or you're just more curious about how it all works for artists), you can check out the Artist Support site. There's a super-handy FAQ page which covers a lot, and answers some very similar questions.
Hope this helps. Feel free to fire more questions this way on the Community too, we'll always be around to help 🙂