New Spotify for Mac: link/file
I know the official update isn't released yet, but a user on here (Javiers) left a link about a month ago on an article posted by the Verge, where you can install the update.
Here is the link
Just uninstall the current Spotify application you have on your Mac, delete it from the trash bin, and install the file on his page and that's it. Enjoy! I love the new look, by the way. :)