How do I clear the Gnome terminal history?

You can use tput reset.

Besides reset and tput reset you can use following shell script.

#!/bin/sh
echo -e \\033c

This sends control characters Esc-C to the console which resets the terminal.

Google Keywords: Linux Console Control Sequences

man console_codes says:

The sequence ESC c causes a terminal reset, which is what you want if the screen is all garbled. The oft-advised "echo ^V^O" will only make G0 current, but there is no guarantee that G0 points at table a). In some distributions there is a program reset(1) that just does "echo ^[c". If your terminfo entry for the console is correct (and has an entry rs1=\Ec), then "tput reset" will also work.

You can use the reset command, that will reset the terminal settings.

I know you're on a gnome terminal, but I thought I'd answer with a tip for others who might be (like me) on a Mac:

If you're using Terminal.app or iTerm.app then Control+L will scroll up so the terminal looks blank, but Cmd+K will actually reset the terminal / clear scroll-back.

Or, if you're able to set keyboard preferences for your terminal you may be able to assign something like Ctrl+K to input echo -e \\033c as was mentioned above.