Whonix has added Monero to its APT repository (you can see that here) so the process is now pretty straightforward:

Download and add the Whonix signing key:

wget https://www.whonix.org/patrick.asc
sudo apt-key --keyring /etc/apt/trusted.gpg.d/whonix.gpg add ~/patrick.asc

Add Whonix's APT repository:

echo "deb https://deb.whonix.org buster main contrib non-free" | sudo tee /etc/apt/sources.list.d/whonix.list

Update your package lists:

sudo apt-get update

Install the Monero GUI:

sudo apt-get install monero-gui

Whonix has added Monero to its APT repository (you can see that here) so the process is now pretty straightforward:

Download and add the Whonix signing key:

wget https://www.whonix.org/patrick.asc
sudo apt-key --keyring /etc/apt/trusted.gpg.d/whonix.gpg add ~/patrick.asc

Add Whonix's APT repository:

echo "deb https://deb.whonix.org bullseye main contrib non-free" | sudo tee /etc/apt/sources.list.d/whonix.list

^{Note: This line previously said "buster" instead of "bullseye" - buster is the old release - see Whonix 15 Deprecation for details}

Update your package lists:

sudo apt-get update

Install the Monero GUI:

sudo apt-get install monero-gui