Run terminal and type:
sudo apt-get update sudo apt-get install software-properties-common sudo apt-add-repository "deb http://repository.spotify.com stable non-free" sudo apt-key adv --keyserver hkp://keyserver.ubuntu.com:80 --recv-keys 94558F59 D2C19886 sudo apt-get update sudo apt-get install spotify-client
In case of a problem please comment below. Official instruction can be found here (it was incomplete at the moment of writing).