How to append new form elements in “Add New” form of Users in WordPress admin panel?

As of WordPress 3.0.0 this action is available at the top of the new user form:

user_new_form_tag

As of WordPress 3.7.0 this action is called at the end of the form (right before submit button):

user_new_form

You will however need to intercept when clicking submit to save any specific user information to the user’s meta