By default, WooCommerce marks the orders as “processing” if the product is physical and virtual, not downloadable. This is because the store owner must still process (ship) the order and manually mark it as "complete."

In most cases, if the payment is successful, you might want to mark them “complete” even before delivering the product.

You can use the WC Auto Complete Order Status Plugin to facilitate this process while you sit back and relax. This plugin is designed to be simple and set-and-forget, and it has no bloat whatsoever. If the order has received payment, the plugin automatically marks it as "complete." It works for all old orders as well as new orders.

If there are many old orders marked as "processing," the plugin uses Action Scheduler to schedule the marking. It marks 10 orders at a time so that you won’t be facing time-out issues, also making it a smooth process.