If you subscribe to the spotify premium service, you can download Spotify songs to the spotify desktop application on your computer, but these downloaded files are offline cached files, and you can only listen to it on the spotify desktop application.
I wanna find some apps to help me download Spotify music to local. Luckily, I find AudFun Spotify downloader, which can download Spotify tracks to local and save tracks as MP3. I have used AudFun Spotify downloader for a while now, and very happy with it.
Quiet straightforward and Fast speed.
Worth a try!