Source: http://tipsonubuntu.com/2016/11/09/install-budgie-desktop-ubuntu-16-04-16-10/
Ubuntu Budgie now is an official Ubuntu flavor. For those who want to try this Gnome 3 based desktop environment, here is how to install Budgie Desktop in Ubuntu 16.04, Ubuntu 16.10. Also a complete uninstall guide is available. Budgie Desktop is a modern desktop features heavy integration with the GNOME stack. It’s the default desktop environment of Ubuntu Budgie (formerly known as Budgie Remix), which now is an official Ubuntu flavor.
Budgie Remix Team has an official PPA repository. So far Ubuntu 16.04, Ubuntu 16.10, and their derivatives are supported.
sudo add-apt-repository ppa:budgie-remix/ppa
Type in your password (no visual feedback) when it asks and hit Enter.
sudo apt update
sudo apt install budgie-desktop-environment
The commands will install the new desktop environments along with new startup splash, GTK login greeter, recommended Gnome libraries, etc.
3. Once installed, log out and select Budgie Desktop session by clicking the logo icon after your username.
sudo apt remove budgie-desktop-environment budgie-desktop && sudo apt autoremove
And the PPA can be removed by going to System Settings -> Software & Updates -> Other Software tab.
sudo apt remove lightdm-gtk-greeter && sudo apt autoremove
sudo update-alternatives --config default.plymouth
Type the number that indicates Ubuntu logo and hit enter.
And apply the plymouth changes via command:
sudo update-initramfs -u
The command takes a few seconds depends on your machine.