Zero-out drive on Linux is done via:

dd if=/dev/zero of=/dev/sdX

where sdX is the device of the drive to delete.

If you're not aware on how to do this, press Ctrl+Alt+T from Ubuntu, and type following:

sudo dd if=/dev/zero of=/dev/sdb

In example above, sdb is the second connected drive.

NB! This will erase your drive completely. Use at your own risk.

EDIT 1:

Optionally, you might want to add status=progress to show progress status:

sudo dd if=/dev/zero of=/dev/sdb status=progress

EDIT 2:

As per comments below, setting the buffer size might significantly speed up the process:

sudo dd if=/dev/zero of=/dev/sdb bs=16M

Please note, however, with a buffer dd will not wait until operation is complete, so afterwards you might need to execute sync command, which synchronizes data on disk with memory.

sudo dd if=/dev/zero of=/dev/sdb bs=16M && sync

What's the purpose of sync? Simple: in case if your storage is slow and power off happens right after dd while disk data is not synchronized, some of the data might be lost. It might be not so relevant for this particular case about zeroing out the drive on PC, but for things like embedded systems with slow flash memories this needs to be considered.