Example of adding a select box to the "General" product data tab.

woo-selectbox.php

<?php
function prefix_add_selectbox() {
  $args = array(
    'id' => 'my_new_select', // required. The meta_key ID for the stored value
    'wrapper_class' => '', // a custom wrapper class if needed
    'desc_tip' => true, // makes your description show up with a "?" symbol and as a tooltip
    'description' => __('My awesome select box', 'your_text_domain'),
    'label' => __( 'My New Select', 'your_text_domain' ),
    'options' => array(
      'value1' => __( 'Text 1', 'your_text_domain' ),
      'value2' => __( 'Text 2', 'your_text_domain' )
    )
  );
  woocommerce_wp_select( $args );
}

add_action( 'woocommerce_product_options_tax', 'prefix_add_selectbox' );

Hi Jan, thanks for this amazing code snippet, is there an option to make the new Field appears in the quick edit page?