:warning: UNMAINTAINED :warning:

I highly recommend you to check out Blur my Shell (GNOME 3.36+)

GNOME Shell Extension - Blyr

Apply a Blur Effect to GNOME Shell UI elements

Screenshots

Activities Background Blur:

Overview with a blur intensity of 10:

Overview with a blur intensity of 30:

Panel Blur:

GNOME Shell 3.26+:

With GNOME Shell version 3.32 the panel transparency was removed. In order to use the blurred panel feature, you can install the Dynamic Panel Transparency extension.

Extension Preferences:

Installation

Official

Install blyr using the official repository: extensions.gnome.org

Manual

git clone https://github.com/yozoon/gnome-shell-extension-blyr.git
cd gnome-shell-extension-blyr/
make local-install

Now just restart the Shell and enable the extension.

To remove the extension just run:

make local-uninstall

Troubleshooting

Some Ubuntu users reported that the preferences dialog didn't appear after opening it from the GNOME Tweaks application. To fix the issue install the gtkclutter bindings as follows:

sudo apt install gir1.2-gtkclutter-1.0