Add zabbix 4 repository (beta is version still numbered as 3.5)

echo "deb http://repo.zabbix.com/zabbix/3.5/ubuntu xenial main" | sudo tee /etc/apt/sources.list.d/zabbix4.list > /dev/null

Add the missing public key for repository with

sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 082AB56BA14FE591

and update the apt package list with

apt-get update

Install the Zabbix server (if mysql has not been installed before, please note down the root password!)

apt-get install mysql-server zabbix-server-mysql zabbix-release

If everything went well, we can also add the Zabbix Web UI (not needed but really, really useful) with

apt-get install zabbix-frontend-php

Now edit /etc/apache2/conf.d/zabbix, uncomment the date.timezone line and set the correct timezone. Mine looks like

  php_value date.timezone Europe/Rome