With a Spotify Premium account, you can play audio files stored on your device through the Local Features on the Spotify app.
Files should be .mp3, .mp4, .m4a
iOS
To activate Local Files on your iPhone:
On the Spotify app, tap Home
Tap Settings
Tap Local Files
Switch on Show audio files from this device
If you want to sync files from your desktop to your iPhone, click OK on the pop-up that asks permission to access your local network.
Connect your phone to the same Wi-Fi network as the computer where you upload the songs.
Open the Spotify app and go to the playlist where you put your local music.
Under the playlist name, tap the download icon. (the downward-pointing arrow)
Once you tap download, Spotify will save every song in the playlist onto your phone. You can move them into your other Spotify playlists.
To sync music from a desktop to an iOS mobile device check out Apple's how to here. Sync music across devices
Android
Tap Home
Tap Settings
Switch to Show audio files from this device
Your stored music should now be in Local Files in your Library.