No deb packages have been released yet for Ubuntu 18.04, so you have to use the script MS provided here. However, you will face the following error immediately:

 fatal error: Python.h: No such file or directory

To resolve this, simply install the python-dev package:

sudo apt install python-dev

Then run the script normally:

curl -L https://aka.ms/InstallAzureCli | bash

Once done, exit the terminal and open a new one.

That’s it! Enjoy!

Sources:

1. https://docs.microsoft.com/en-us/cli/azure/install-azure-cli-linux?view=azure-cli-latest
2. https://github.com/Azure/azure-docs-cli-python/issues/755
3. https://github.com/benhoyt/scandir/issues/85