First we install the required packages. As root do:

apt-get install unattended-upgrades

Create the file: /etc/apt/apt.conf.d/20auto-upgrades and add the following content to it:

APT::Periodic::Update-Package-Lists "1";
APT::Periodic::Unattended-Upgrade "1";

Replace the file /etc/apt/apt.conf.d/50unattended-upgrades and add the following to it to upgrade everything. Here you can also add excludes if there are packages you don't want upgraded automatically.

Unattended-Upgrade::Origins-Pattern {
        "o=*";
};
Unattended-Upgrade::Automatic-Reboot "false";
Unattended-Upgrade::Mail "root";

That's it! Now you'll receive an e-mail every time your system upgrades itself.