– Tested with Ubuntu 16.04 (Xenial) LTS and Zabbix Controller 5.8.28 on September 2018 –

echo 'deb http://www.ubnt.com/downloads/unifi/debian stable ubiquiti' | sudo tee /etc/apt/sources.list.d/100-ubnt-unifi.list
sudo apt-key adv --keyserver keyserver.ubuntu.com --recv 06E85760C0A52C50
sudo apt update

sudo apt install openjdk-8-jre
sudo apt install unifi

Have a log at syslogs with

 sudo tail -f /var/log/syslog

If you see errors like

[...] unifi error: Service killed by signal 11

you have encoutered a know bug. To solve the issue type

echo "JSVC_EXTRA_OPTS=\"\$JSVC_EXTRA_OPTS -Xss1280k\"" | sudo tee -a /etc/default/unifi

and restart the controller with

sudo systemctl stop unifi
sudo systemctl start unifi

Note that unifi restart could take a lot of time. If you are in hurry, you can kill stuck unifi processes manually with kill -9 before restarting the service (or reboot the machine :)

Now you can point your browser to

https://your-server-address:8443/