add_filter(‘woocommerce_order_item_needs_processing’, ‘auto_complete_free_downloadable’, 10, 3);
function auto_complete_free_downloadable($needs_processing, $product, $order) {
if ($product->is_downloadable() && $order->get_total() == 0) {
return false;
}
return $needs_processing;
}

add_action(‘woocommerce_thankyou’, ‘auto_complete_order_for_free_products’);
function auto_complete_order_for_free_products($order_id) {
if (!$order_id) return;

$order = wc_get_order($order_id);
if ($order->get_total() == 0) {
$order->update_status(‘completed’);
}
}