Because it is not available via the default repositories of Ubuntu and Linux Mint, we have to add the Elementary OS PPA, update the local repository index and install the elementary-desktop package. Like this:
$ sudo add-apt-repository -y ppa:elementary-os/stable
$ sudo apt-get update
$ sudo apt-get install elementary-desktop
To get over the wallpaper bug, open a terminal and paste the below oneliner:
$ gsettings set org.gnome.settings-daemon.plugins.background active true
Also, if you want a closer look to Elementary OS, you should install plank, from ricotz PPA:
$ sudo add-apt-repository ppa:ricotz/docky
$ sudo apt-get update
$ sudo apt-get install plank
Next, install the Elementary Tweaks tool in order to tweak your system:
$ sudo add-apt-repository ppa:versable/elementary-update
$ sudo apt-get update
$ sudo apt-get install elementary-tweaks
Source: http://linuxg.net/how-to-install-elementary-oss-pantheon-desktop-environment-on-ubuntu-and-linux-mint/