– Tested with Ubuntu 16.04 (Xenial) LTS / Debian 9 and Zabbix Agent 4.0 beta 1 on September 2018 –

First of all, add Zabbix 4 repository (4 is in beta, hence is version still numbered as 3.5). For Ubuntu 16.04 use

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

(build are availble for bionic, trusty, and xenial - set the repo accordingly)

For Debian 9 use

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

(but jessie and wheezy builds are available, too).

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

sudo apt-get update

Install the Zabbix Agent

sudo apt-get install zabbix-agent

Edit your local configuration with

sudo vim /etc/zabbix/zabbix_agentd.conf.d/mysetup.conf

and set your custom parameters (at least the address of the zabbix server)

Server=1.2.3.4,zabbix.example.com

Finally restart the agent with

sudo systemctl restart zabbix-agent