You can use Wordpress dedicated template_redirect
hook to make a redirection after a purchase and pass any order data through the url like in this example:
add_action( 'template_redirect', 'order_received_redirection' );
function order_received_redirection() {
// Only on "Order received" page
if( is_wc_endpoint_url('order-received') ) {
global $wp;
$order_id = absint( $wp->query_vars['order-received'] );
$order = wc_get_order($order_id);
$key = isset( $_GET['key'] ) ? wc_clean( $_GET['key'] ) : $order->get_order_key();
$total = $order->get_total();
// HERE BELOW Set your redirection url
$url_redirect = 'http://www.my-domain.com/?orderid='.$order_id . '&key=' . $key . '&total=' . $total;
// Redirect
wp_redirect( $url_redirect );
exit(); // Always exit
}
}
Code goes in function.php file of your active child theme (active theme). Tested and works.
Related: How to get WooCommerce order details