It seems that my edit to your answer was declined, so here you go.
All that was missing was the $priority and $accepted_args parameters for the add_action() calls, and the the fixed code below should accomplish what you require.
remove_action( 'add_option_new_admin_email', 'update_option_new_admin_email' );
remove_action( 'update_option_new_admin_email', 'update_option_new_admin_email' );
/**
* Disable the confirmation notices when an administrator
* changes their email address.
*
* @see http://codex.wordpress.com/Function_Reference/update_option_new_admin_email
*/
function wpdocs_update_option_new_admin_email( $old_value, $value ) {
update_option( 'admin_email', $value );
}
add_action( 'add_option_new_admin_email', 'wpdocs_update_option_new_admin_email', 10, 2 );
add_action( 'update_option_new_admin_email', 'wpdocs_update_option_new_admin_email', 10, 2 );