Assigning Page its own template

Fairly new to wordpress (by no means an advanced user yet). Creating my first real custom theme to be used as a website (I have created websites using HTML and CSS before).

I have created a custom page.php template to be used for the majority of the pages on the website. However I want to have a gallery page that uses its own unique template (Lets call it gallery.php) instead of the page.php template.

Id there a way to do this from inside the WP-Admin Dashboard? Or does it need to be hard coded in somewhere?

Any help would be appreciated!